Technical information
Selecting Centrifugal Pumps
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4th completely revised and ex panded edition 2005 Layout, drawings and composition: KSB Aktiengesellschaft, Media Production V51 ISBN 3000178414
Contents Table of contents
1 2 3
Nomenclature...................................................................6 Pump Types .................................................................8–9 Selection for Pumping Water...........................................10
3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.2.1 3.2.1.2.2 3.2.2 3.3 3.3.1 3.3.2 3.3.3 3.3.3.1 3.3.3.2 3.3.3.3 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.4.7 3.4.8 3.4.9 3.4.10 3.5 3.5.1 3.5.1.1 3.5.1.2 3.5.2 3.5.3 3.6
Pump Data................................................................................10 Pump Flow Rate.......................................................................10 Developed Head and Developed Pressure of the Pump..............10 Efficiency and Input Power.......................................................10 Speed of Rotation.....................................................................11 Specific Speed and Impeller Type...............................................11 Pump Characteristic Curves......................................................13 System Data..............................................................................16 System Head ............................................................................16 Bernoulli’s Equation..................................................................16 Pressure Loss Due to Flow Resistances......................................18 Head Loss in Straight Pipes.......................................................18 Head Loss in Valves and Fittings...............................................22 System Characteristic Curve......................................................26 Pump Selection..........................................................................28 Hydraulic Aspects.....................................................................28 Mechanical Aspects...................................................................29 Motor Selection........................................................................29 Determining Motor Power........................................................29 Motors for Sealless Pumps.......................................................31 Starting Characteristics.............................................................31 Pump Performance and Control................................................34 Operating Point........................................................................34 Flow Control by Throttling.......................................................34 Variable Speed Flow Contol......................................................35 Parallel Operation of Centrifugal Pumps...................................36 Series Operation........................................................................38 Turning Down Impellers...........................................................38 Underfiling of Impeller Vanes...................................................39 Preswirl Control of the Flow....................................................39 Flow Rate Control or Change by Blade Pitch Adjustment.........39 Flow Control Using a Bypass....................................................40 Suction and Inlet Conditions.....................................................41 The NPSH Value of the System: NPSHa ...................................41 NPSHa for Suction Lift Operation............................................43 NPSHa for Suction Head Operation..........................................44 The NPSH Value of the Pump: NPSHr......................................44 Corrective Measures.................................................................45 Effect of Entrained Solids..........................................................47
4
Special Issues when Pumping Viscous Fluids...................48
4.1 4.2 4.2.1 4.2.2 4.3 4.3.1 4.3.2
The Shear Curve.......................................................................48 Newtonian Fluids......................................................................50 Influence on the Pump Characteristics.......................................50 Influence on the System Characteristics.....................................54 NonNewtonian Fluids.............................................................54 Influence on the Pump Characteristics.......................................54 Influence on the System Characteristics.....................................55
Contents
Tables
5
Special Issues when Pumping Gasladen Fluids...............56
6
Special Issues When Pumping Solidsladen Fluids...........57
6.1 6.2 6.3 6.4 6.5
Settling Speed............................................................................57 Influence on the Pump Characteristics.......................................58 Influence on the System Characteristics.....................................59 Operating Performance.............................................................59 Stringy, Fibrous Solids...............................................................59
7
The Periphery.................................................................62
7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.3 7.4 7.5 7.6
Pump Installation Arrangements...............................................61 Pump Intake Structures.............................................................61 Pump Sump...............................................................................61 Suction Piping...........................................................................62 Intake Structures for Tubular Casing Pumps.............................64 Priming Devices........................................................................65 Arrangement of Measurement Points........................................67 Shaft Couplings.........................................................................68 Pump Nozzle Loading...............................................................69 National and International Standards and Codes......................69
8 9 10
Calculation Examples (for all equations numbered in bold typeface).................71 Additional Literature......................................................79 Technical Annex (Tables, Diagrams, Charts)..................80
Tab. 1: Tab. 2: Tab. 3:
Centrifigal pump classification....................................................8 Reference speeds of rotation.....................................................11 Approximate average roughness height k for pipes...................20
Tab. 4:
Inside diameter d and wall thickness s in mm and weight of
Tab. 5: Tab. 6: Tab. 7: Tab. 8: Tab. 9: Tab. 10: Tab. 11: Tab. 12: Tab. 13:
Tab. 14:
typical commercial steel pipes and their water content............20 Loss coefficients ζ for various types of valves and fittings.........23 Loss coefficients ζ in elbows and bends.....................................24 Loss coefficients ζ for fittings...............................................24/25 Loss coefficients ζ for adapters..................................................25 Types of enclosure for electric motors to EN 60 529 and DIN/VDE 0530, Part 5.............................................................30 Permissible frequency of starts Z per hour for electric motors...30 Starting methods for asynchronous motors...............................32 Vapour pressure, density and kinematic viscosity of water at saturation conditions as a function of the temperature..............42 Influence of the altitude above mean sea level on the annual average atmospheric pressure and on the corresponding boiling point…..........................................................................43 Minimum values for undisturbed straight lengths of piping at measurement points in multiples of the pipe diameter D.......67
1
Nomenclature
1 Nomenclature
A A
m2 m
Area Distance between measuring point and pump flange a m, mm Width of a rectangular elbow B m, mm Vertical distance from suction pipe to floor Cv gpm Flow coefficient for valves, defined as the flow of water at 60 °F in US gallons/minute at a pressure drop of 1 lb/in2 across the valve cD Resistance coefficient of a sphere in water flow cT (%) Solids content in the flow D m (mm) Outside diameter; maximum diameter DN (mm) Nominal diameter d m (mm) Inside diameter; minimum diameter ds m (mm) Grain size of solids d50 m (mm) Mean grain size of solids F N Force f Throttling coefficient of an orifice fH Conversion factor for head (KSB system) fQ Conversion factor for flow rate (KSB system) fη Conversion factor for efficiency (KSB system) g m/s2 Gravitational constant = 9.81 m/s2 H m Head; discharge head Hgeo m Geodetic head Hs m Suction lift Hs geo m Vertical distance between water level and pump reference plane for suction lift operation Hz geo m Vertical distance between pump reference plane and water level for positive inlet pressure operation HL m Head loss H0 m Shutoff head (at Q = 0) I A Electric current (amperage) K Dimensionless specific speed, type number k mm, µm Mean absolute roughness k Conversion factors kQ, kH, kη (HI method) 3 kv m /h Metric flow factor for valves, defined as the flow of water at 20 °C in cubic metres per hour at a pressure drop of 1 bar L m Length of pipe Ls m Straight length of airfilled pipe M Nm Moment NPSHr m NPSH required by the pump NPSHa m NPSH available Ns Specific speed in US units n min–1 (rpm) Speed of rotation s–1 (rev/s) nq min–1 Specific speed in metric units P kW (W) Power; input power
1
Nomenclature
pe PN (bar) ∆p bar (Pa)
Pressure in suction or inlet tank Nominal pressure Pressure rise in the pump; pressure differential (Pa ≡ N/m2) p bar (Pa) Pressure (Pa ≡ N/m2 = 10–5 bar) pb mbar (Pa) Atmospheric pressure (barometric) pL bar (Pa) Pressure loss pv bar (Pa) Vapour pressure of fluid pumped Q m3/s, m3/h Flow rate / capacity (also in litre/s) qair % Air or gas content in the fluid pumped Qoff m3/h Flow rate at switchoff pressure 3 Qon m /h Flow rate at startup pressure R m (mm) Radius Re Reynolds number S m Submergence (fluid level above pump); immersion depth s mm Wall thickness s’ m Difference of height between centre of pump impeller inlet and centre of pump suction nozzle T Nm Torque t °C Temperature U m Length of undisturbed flow U m Wetted perimeter of a flow section 3 VB m Suction tank volume VN m3 Useful volume of pump sump v m/s Flow velocity w m/s Settling velocity of solids y mm Travel of gate valve; distance to wall Z 1/h Switching cycle (frequency of starts) z Number of stages zs,d m Height difference between pump discharge and suction nozzles α ° δ ° ζ η (%) η Pa s λ m2/s kg/m3 τ N/m2 τf N/m2 ϕ
ψ
Angle of change in flow direction; opening angle Angle of inclination Loss coefficient Efficiency Dynamic viscosity Pipe friction factor Kinematic viscosity Density Shear stress Shear stress at yield point Temperature factor; opening angle of a butter fly valve; cos ϕ: power factor of asynchronous motors Head coefficient (dimensionless head generated by impeller)
Indices, Subscripts a
At outlet crosssection of the system; branching off Bl Referring to orifice bore d On discharge side; at dis charge nozzle; flowing through dyn Denoting dynamic com ponent At the narrowest crossE section of valves (Table 5) E At suction pipe or bell mouth inlet e At inlet crosssection of system, e. g. in suction or inlet tank f Referring to carrier fluid H Horizontal in Referring to inlet flow K Referring to curvature L Referring to losses m Mean value max Maximum value min Minimum value N Nominal value opt Optimum value; at best efficiency point (BEP) P Referring to pump p Referring to pressure Reduced, for cutdown imr peller or impeller vanes s On suction side; at suc tion nozzle s Referring to solids stat Static component sys Referring to system / installation t Referring to impeller prior to trimming V Vertical w Referring to water z Referring to viscous fluid 0 Basic position, referred to individual sphere 1, 2, 3 Consecutive numbers; items I, II Number of pumps oper ated
2
Pump Types (Examples)
2 Pump Types
– the position of the shaft (hori zontal / vertical),
Other pump classification features include:
Typical selection criteria for centrifugal pumps are their design data (flow rate or capac ity Q, discharge head H, speed of rotation n and NPSH), the properties of the fluid pumped, the application, the place of installation and the applicable regulations, specifications, laws and codes. KSB offers a broad range of pump types to meet the most varied requirements.
– the pump casing (radial, e. g. volute casing / axial, e. g. tubular casing),
– the mode of installation, which is dealt with in section 7.1,
– the number of impeller entries (single entry / double entry), – the type of motor (dry mo tor / dry rotor motor, e. g. submerged motor / wet rotor motor, e. g. canned motor, submersible motor). These features usually determine what a pump type or series looks like. An overview of typi cal designs according to classi fication features is given below (Table 1 and Figs. 1a to 1p).
Main design features for classifi cation are: – the number of stages (singlestage / multistage),
Table 1: Centrifugal pump classification
– the nominal diameter (for the pump size, as a function of the flow rate), – the rated pressure (for the wall thickness of casings and flanges), – the temperature (for example for the selection of cooling equipment for shaft seals), – the fluid pumped (abrasive, aggressive, toxic fluids), – the type of impeller (radial flow / axial flow depending on the specific speed), – the selfpriming ability,
Number of stages
Single stage
Multistage
Shaft position
Horizontal
Horiz. Vertic.
Casing design
Radial Axial Radial Axial Stage casing
Vertical
– the casing partition, the posi tion of the pump nozzles, an outer casing, etc.
Impeller entries 1 2 1 1 2 1 1 1 Motor type, Fig. 1.. Dry (standardized) motor Magnetic drive Submerged dry rotor motor (See 3.3.2) Wet rotor motor (See 3.3.2)
a b c i
d e f
g
h
j
k
l
m
n
o
p
a
b
2
Pump Types (Examples)
c
d
e
f
g
h
i
j
k
l
m
n
o
p
Fig 1 (a to p): Centrifugal pump classification acc. to Table 1
3
Flow Rate · Head · Efficiency · Input Power
3 Selection for Pumping Water This section applies mainly to pumping water; the particulari ties of pump selection for other media are treated in sections 4, 5 and 6. 3.1 Pump Data 3.1.1 Pump Flow Rate The pump flow rate or capacity Q is the useful volume of fluid delivered to the pump discharge nozzle in a unit time in m3/s (l/s and m3/h are also used in practice, as are GPM in the US). The flow rate changes propor tionally to the pump speed of rotation. Leakage flow as well as the internal clearance flows are not considered part of the pump flow rate. 3.1.2 Developed Head and Developed Pressure of the Pump The total developed head H of a pump is the useful mechanical energy in Nm transferred by the pump to the flow, per weight of fluid in N, expressed in Nm/N = m (also used to be called “metres of fluid”)1). The head develops proportionally to the square of the impeller’s speed of rotation and is inde pendent of the density of the fluid being pumped. A given centrifugal pump will impart the 1)
In the US, the corresponding units are ftlbf/lbm, i. e. 1 foot head = 1 footpoundforce per pound mass; the numerical value of head and specific work are identical.
10
same head H to various fluids (with the same kinematic viscos ity ) regardless of their density . This statement applies to all centrifugal pumps. The total developed head H manifests itself according to Bernoulli’s equation (see section 3.2.1.1) as – the pressure head Hp propor tional to the pressure differ ence between discharge and suction nozzles of the pump, – the geodetic head zs,d (Figs. 8 and 9), i.e., the difference in height between discharge and suction nozzles of the pump and – the difference of the kinetic energy head (vd2vs2)/2g be tween the discharge and suc tion nozzles of the pump. The pressure rise Δp in the pump (considering the location of the pressure measurement taps according to section 7.3!) is determined solely by the pres sure head Hp along with the fluid density r according to the equation Δp = · g · [H  zs,d  (vd2vs2)/2g] (1)
where Density of the fluid being pumped in kg/m3 g
Gravitational constant 9.81 m/s2
H Total developed head of the pump in m zs,d Height difference between pump discharge and suction nozzles in m (see Figs. 8 and 9)
vd Flow velocity in the discharge nozzle = 4 Q/pdd2 in m/s vs Flow velocity in the suction nozzle = 4 Q/pds2 in m/s Q Flow rate of the pump at the respective nozzle in m3/s d
Inside diameter of the re spective pump nozzle in m
Δp Pressure rise in N/m2 (for conversion to bar: 1 bar = 100 000 N/m2) Highdensity fluids therefore increase the pressure rise and the pump discharge pressure. The discharge pressure is the sum of the pressure rise and the inlet pressure and is limited by the strength of the pump casing. The effect of temperature on the pump’s strength limits must also be considered. 3.1.3 Efficiency and Input Power The input power P of a pump (also called brake horsepower) is the mechanical power in kW or W taken by the shaft or coupling. It is proportional to the third power of the speed of rotation and is given by one of the following equations:
3
Efficiency · Input Power · Speed · Specific Speed
P =
·g·Q·H in W η
·g·Q·H in kW = 1000 · η
where Density in kg/m3 in kg/m3 Q Flow rate in m3/s in m3/s g Gravitational constant = 9.81 m/s2 H Total developed head in m η Efficiency between 0 and <1 (not in %) The pump efficiency η is given with the characteristic curves (see section 3.1.6). The pump input power P can also be read with sufficient accuracy directly from the charac
3.1.4 Speed of Rotation When using threephase current motors (asynchronous squirrel
·Q·H = in kW 367 · η (2) in kg/dm3 in m3/h
teristic curves (see section 3.1.6) for density = 1000 kg/m3. For other densities , the input power P must be changed in proportion. Pumping media which are more
cage motors to IEC standards) the following speeds of rotation are taken as reference for pump operation:
Table 2: Reference speeds of rotation Number 2 of poles
4
6
8 10 12 14
Frequency Reference speeds for the characteristic curve documen tation in min–1 (rpm) For 50 Hz 2900 1450
960
For 60 Hz 3500 1750 1160
In practice the motors run at slightly higher speeds (which depend on the power output and on the make) [1], which the pump manufacturer may con sider for the pump design and selection when the customer agrees. In this case, the affinity laws described in section 3.4.3 are to be applied. The charac teristic curves of submersible motor pumps and submersible borehole pumps have already
725
580
480
415
875
700
580
500
been matched to the actual speed of rotation. When using motor speed con trollers (for example phase angle control for ratings up to a few kW or, in most other cases, frequency inverters), gearboxes, belt drives or when using tur bines or internal combustion engines as drivers, other pump speeds are possible.
viscous than water (see section 4) or have high concentra tions of entrained solids (see section 6) will require a higher input power. This is, for ex ample, the case when pumping sewage or waste water, see sec tion 3.6. The pump input power P is linearly proportional to the fluid density . For highdensity fluids the power limits of the motor (section 3.3.3) and the torque limits (for the loading on coupling, shaft and shaft keys) must be considered.
3.1.5 Specific Speed and Impeller Type The specific speed nq is a para meter derived from a dimen sional analysis which allows a comparison of impellers of vari ous pump sizes even when their operating data differ (flow rate Qopt, developed head Hopt, ro tational speed n at the point of best efficiency ηopt). The specific speed can be used to classify the optimum impeller design (see Fig. 2) and the corresponding pump characteristic curve (see section 3.1.6, Fig. 5). nq is defined as the theoreti cal rotational speed at which a geometrically similar impeller would run if it were of such a size as to produce 1 m of head at a flow rate of 1 m3/s at the best efficiency point. It is ex pressed in the same units as the speed of rotation. The spe cific speed can be made a truly
11
3
Specific Speed
dimensionless characteristic parameter while retaining the same numerical value by using
√ Qopt/1 nq = n · (Hopt/1)3/4
the definition in the righthand version of the following equa tion [2]:
√ Qopt = 333 · n · (g · Hopt)3/4
where Qopt in m3/s Hopt in m n in rpm nq in metric units
(3)
Qopt in m3/s = Flow rate at ηopt Hopt in m = Developed head at ηopt n in rev/s = Pump speed nq Dimensionless parameter g Gravitational constant 9.81 m/s2
For multistage pumps the developed head Hopt at best efficiency for a single stage and for doubleentry impellers, the optimum flow rate Qopt for only one im peller half are to be used. As the specific speed nq in creases, there is a continuous change from the originally radial exits of the impellers to
“mixed flow” (diagonal) and eventually axial exits (see Fig. 2). The diffuser elements of radial pump casings (e.g. volutes) be come more voluminous as long as the flow can be carried off radially. Finally only an axial exit of the flow is possible (e. g. as in a tubular casing).
Approximate reference values: nq up to approx. 25 up to approx. 40 up to approx. 70 up to approx. 160 approx. from 140 to 400
Radial high head impeller Radial medium head impeller Radial low head impeller Mixed flow impeller Axial flow impeller (propeller)
Using Fig. 3 it is possible to de termine nq graphically. Further types of impellers are shown in Fig. 4: Star impellers are used in selfpriming pumps. Peripheral impellers extend the speci fic speed range to lower values down to approximately nq = 5 (peripheral pumps can be de signed with up to three stages). For even lower specific speeds, rotary (for example progressive cavity pumps with nq = 0.1 to 3) or reciprocating positive dis placement pumps (piston pumps) are to be preferred. The value of the specific speed is one of the influencing para meters required when convert ing the pump characteristic curves for pumping viscous or solidsladen media (see sections 4 and 6). In Englishlanguage pump lit erature the true dimensionless specific speed is sometimes des ignated as the “type number K”. In the US, the term Ns is used, which is calculated using gal lons/min (GPM), feet and rpm. The conversion factors are: K = nq / 52.9 Ns = nq / 51.6
(IGHHEAD EDIUMHEAD IMPELLER IMPELLER NQUPTO
UPTO
,OWHEAD IMPELLER
IXEDFLOW IMPELLER
UPTO
UPTO
!XIALFLOW PROPELLER TO RPM
Fig. 2: Effect of the specific speed nq on the design of centrifugal pump impellers. The diffuser elements (casings) of single stage pumps are outlined.
12
(4)
3
Specific Speed · Impeller Types · Characteristic Curves
Fig. 3: Nomograph to determine specific speed nq (enlarged view on p. 80) Example: Qopt = 66 m3/h = 18.3 l/s; n = 1450 rpm, Hopt = 17.5 m. Found: nq = 23 (metric units). 3.1.6 Pump Characteristic Curves
Radial impeller *)
Radial doubleentry impeller*)
Closed (shrouded) mixed flow impeller *) Star impeller for side channel pump (selfpriming)
Open (unshrouded) mixed flow impeller
Unlike positive displacement pumps (such as piston pumps), centrifugal pumps deliver a var iable flow rate Q (increasing with decreasing head H) when operating at constant speed. They are therefore able to ac commodate changes in the system curve (see section 3.2.2). The input power P and hence the efficiency η as well as the NPSHr (see section 3.5.4) are dependent on the flow rate.
Peripheral pump impeller for very low specific speed (nq ≈ 5 to 0)
Axial flow propeller
*) Plan view shown without front shroud
Fig. 4: Impeller types for clear liquids
13
3
Characteristic Curves
The relationship of these val ues is shown graphically in the pump characteristic curves, whose shape is influenced by the specific speed nq and which document the performance of a centrifugal pump (see Fig. 5 for a comparison of characteristics and Fig. 6 for examples). The head curve of the pump is also referred to as the H/Q curve.
300 300
( (OPT
150
Operating limit for low input power
70 40
for high input power
0 0OPT
25
150
70 40 25
11OPT
H HOPT
11OPT
The H/Q curve can be steep or flat. For a steep curve, the flow rate Q changes less for a given change of developed head ΔH than for a flat curve (Fig. 7). This can be advantageous when controlling the flow rate.
300
NPSHr NPSHr opt
150 25
300 70
25
25 40
70
40 25
300
150 300
11OPT
11OPT
Fig. 5: Effect of specific speed nq on centrifugal pump characteristic curves (Not drawn to scale! For NPSHr , see section 3.5.4).
Head H [m]
60 50
Efficiency H [%]
70 60 50 40 30
80 70
80
0 30 20
60 50 40
20
40
60
80
100 120 140 160
Flow rate Q [m3/h]
>
Operating limit
70 60 50 40 30
15 10 5 0 17 16 15 14 13
n = 980 min–1
90
NPSHr [m]
NPSHr [m]
5
10 0
90
30
20 10
Power P [kW]
Power P [kW]
NPSHr [m]
Efficiency H [%]
40 80
n = 1450 min–1
15 10 5
100 80 60 40 20 0
Power P [kW]
Head H [m]
70
20 18 16 14 12 10 8 6 4 2
24 22 20 18 16 14 12 10 8 6
Head H [m]
n = 2900 min–1
80
Efficiency H [%]
90
0
100
200
300
400
Flow rate Q [m3/h]
500 550
L
0
500
1000
1500
2000
Flow rate Q [m3/h]
Fig. 6: Three examples of characteristic curves for pumps of differing specific speeds. a: radial impeller, nq ≈ 20; b: mixed flow impeller, nq ≈ 80; c: axial flow impeller, nq ≈ 200. (For NPSHr see section 3.5.4)
14
2500
3000
V
3
Characteristic Curves
Fig. 7: Steep, flat or unstable characteristic curve
is unstable (shown by the dash line in Fig. 7). This type of pump characteristic curve need only be avoided when two intersections with the system curve could result, in particular when the pump is to be used for parallel operation at low flow rates (see section 3.4.4) or when it is pumping into a vessel which can store energy (accumulator filled with gas or steam). In all other cases the unstable curve is just as good as the stable charac teristic.
H/Q characteristics normally have a stable curve, which means that the developed head falls as the flow rate Q in
Unless noted otherwise, the characteristic curves apply for the density and the kinematic viscosity of cold, deaerated water.
AXIMUM
(EAD(
3TEEPCHARACTERISTICCURVE &LATCHARACTERISTICCURVE
5NSTABLE REGION
( 1STEEP 1FLAT &LOWRATE1
creases. For low specific speeds, the head H may – in the low flow range – drop as the flow rate Q decreases, i. e., the curve
15
3
System Head · Bernoulli
PA A
PA
A
VA !
A
VA
"
VA
#
(GEO VD
ZS D VS
(SGEO PE E
VE $
E
VE %
Fig. 8: Centrifugal pump system with variously designed vessels in suction lift operation A = Open tank with pipe ending below the water level B = Closed pressure vessel with free flow from the pipe ending above the water level C = Closed pressure vessel with pipe ending below the water level D = Open suction/inlet tank E = Closed suction/inlet tank va and ve are the (usually negligible) flow velocities at position a in tanks A and C and at position e in tanks D and E. In case B, va is the nonnegligible exit velocity from the pipe end at a .
3.2.1.1 Bernoulli’s Equation
static pressure and kinetic energy form. The system head Hsys for an assumed frictionless, inviscid flow is composed of the following three parts (see Figs. 8 and 9):
Bernoulli’s equation expresses the equivalence of energy in geodetic (potential) energy,
• Hgeo (geodetic head) is the difference in height between the liquid level on the inlet
3.2 System Data 3.2.1 System Head
16
and discharge sides. If the dis charge pipe ends above the liquid level, the centre of the exit plane is used as reference for the height (see Figs 8B and 9B). • (pa  pe)/( · g) is the pressure head difference between the inlet and outlet tank, applic
3
System Head · Bernoulli
PA A
PA
A
VA !
A
VA
"
VA
# (GEO PE
E
VE $
E
VE %
VD
(ZGEO ZS D
VS
Fig. 9: Centrifugal pump system with variously designed vessels in suction head (positive inlet pressure) operation. Legend as in Fig. 8.
able when at least one of the tanks is closed as for B, C or E (see Figs. 8B, C, E, 9B, C, E). • (va2ve2)/2g is the difference in the velocity heads between the tanks. For a physically real flow, the friction losses (pressure head losses) must be added to these components: ∑HL is the sum of the head losses (flow resistance in the
piping, valves, fittings, etc in the suction and discharge lines as well as the entrance and exit losses, see section 3.2.1.2), and
is referred to as the system pres sure loss. The sum of all four components yields the system head Hsys:
Hsys = Hgeo + (pa – pe) / ( · g) + (va2ve2)/2g + ∑HL
(5)
where all the heads H are in m, all the pressures p are in Pa (1 bar = 100 000 Pa), all velocities v are in m/s, the density is in kg/m3, the gravitational constant is g = 9.81 m/s2.
17
3
System Head · Pressure Loss · Head Loss
The difference of the velocity heads can often be neglected in practice. When at least one tank is closed as for B, C or E (see Figs. 8B, C, E, 9B, C, E), Eq. 5 can be simplified as
3.2.1.2 Pressure Loss Due to Flow Resistances
(6)
and further simplified when both tanks are open as for A and D (see Figs. 8A, D and 9A, D) as Hsys ≈ Hgeo + ∑HL
The head loss for flow in straight pipes with circular crosssections is given in general by
The pressure loss pL is caused by wall friction in the pipes and flow resistances in valves, fit tings, etc. It can be calculated from the head loss HL, which is independent of the density , using the following equation:
Hsys ≈ Hgeo + (pa – pe)/( · g) +∑HL
3.2.1.2.1 Head Loss in Straight Pipes
pL = · g · HL
H L = λ ·
(9)
where λ Pipe friction factor according to Eqs. (12) to (14) L Length of pipe in m d Pipe inside diameter in m v Flow velocity in m/s (= 4Q/πd2 for Q in m3/s) g Gravitational constant 9.81 m/s2
(8)
where Density in kg/m3 g Gravitational constant 9.81 m/s2 HL Head loss in m pL Pressure loss in Pa (1 bar = 100 000 Pa)
(7)
L v2 · d 2g
Fig. 10: Pipe friction factor λ as a function of the Reynolds number Re and the relative roughness d/k (enlarged view on p. 81)
DK L 2E
&ULLYROUGHK ,IM ITIN
G
0IPEFRICTIONFACTORL
CU
RVE
LAMINAR
TURBULENT
(YD
RAU
LICA L
LYS M
OOT
HK
2ECRIT
2EYNOLDSNUMBER2E
18
3
Head Loss in Straight Pipes
For pipes with noncircular crosssections the following applies: d = 4A/U
(10)
where A Crosssectional flow area in m2 U Wetted perimeter of the crosssection A in m; for open channels the free fluid surface is not counted as part of the perimeter. Recommended flow velocities for cold water Inlet piping 0.7 – 1.5 m/s Discharge piping 1.0 – 2.0 m/s for hot water Inlet piping 0.5 – 1.0 m/s Discharge piping 1.5 – 3.5 m/s The pipe friction factor λ has been determined experimentally and is shown in Fig. 10. It varies with the flow conditions of the liquid and the relative rough ness d/k of the pipe surface. The flow conditions are expressed according to the affinity laws (dimensional analysis) using the Reynolds’ number Re. For cir cular pipes, this is: Re = v · d/
(11)
where v Flow velocity in m/s (= 4Q/πd2 for Q in m3/s) d Pipe inside diameter in m Kinematic viscosity in m2/s (for water at 20 °C exactly 1.00 · (10)–6 m2/s). For noncircular pipes, Eq. 10 is to be applied for determining d. For hydraulically smooth pipes (for example drawn steel tubing
or plastic pipes made of poly ethylene (PE) or polyvinyl chlor ide (PVC)) or for laminar flow, λ can be calculated: In the laminar flow region (Re < 2320) the friction factor is independent of the roughness: λ = 64/Re
(12)
For turbulent flow (Re > 2320) the test results can be repre sented by the following empiri cal relationship defined by Eck (up to Re < 108 the errors are smaller than 1%): 0.309 Re 2 (lg ) 7
λ=
(13)
In Fig. 10 it can be seen that the pipe friction factor depends on another dimensionless para meter, the relative roughness of the pipe inner surface d/k; k is the average absolute roughness of the pipe inner surface, for which approximate values are given in Table 3. Note: both d and k must be expressed in the same units, for example mm! As shown in Fig. 10, above a limiting curve, λ is dependent only on the relative roughness d/k. The following empirical equation by Moody can be used in this region: 3
λ = 0.0055 + 0.15/ (d/k) (14) For practical use, the head losses HL per 100 m of straight steel pipe are shown in Fig. 11 as a function of the flow rate Q and pipe inside diameter d. The values are valid only for cold,
clean water or for fluids with the same kinematic viscosity, for completely filled pipes and for an absolute roughness of the pipe inner surface of k = 0.05 mm, i.e., for new seamless or longi tudinally welded pipes. (For the pipe inside diameters, see Table 4). The effect of an increased surface roughness k will be de monstrated in the following for a frequently used region in Fig. 11 (nominal diameter 50 to 300 mm, flow velocity 0.8 to 3.0 m/s). The darkshaded region in Fig. 11 corresponds to the similarly marked region in Fig. 10 for an absolute rough ness k = 0.05 mm. For a rough ness increased by a factor 6 (slightly incrusted old steel pipe with k = 0.30 mm), the pipe friction factor λ (proportional to the head loss HL) in the lightly shaded region in Fig. 10 is only 25% to 60% higher than before. For sewage pipes the increased roughness caused by soiling must be taken into considera tion (see section 3.6). For pipes with a large degree of incrusta tion, the actual head loss can only be determined experimen tally. Deviations from the no minal diameter change the head loss considerably, since the pipe inside diameter enters Eq. (9) to the 5th power! (For example, a 5% reduction in the inside dia meter changes the head loss by 30%). Therefore the nominal diameter may not be used as the pipe inside diameter for the calculations!
19
3
Head Loss in Straight Pipes · Dimensions and Weights of Steel Pipes
Table 3: Approximate average roughness height k (absolute roughness) for pipes *«iÊ>ÌiÀ>Ê
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Table 4: Inside diameter d and wall thickness s in mm and weight of typical commercial steel pipes and their water content in kg/m to ENV 10 220 (formerly DIN ISO 4200). D = outside diameter, s = wall thickness DN D
All dimensions in mm Seamless Welded s * d s ** d
Seamless pipe weight in kg/m Pipe Water
Welded pipe weight in kg/m Pipe Water
15 21.3 2.0 17.3 1.8 17.7 0.952 0.235 0.866 0.246 20 26.9 2.0 22.9 1.8 23.3 1.23 0.412 1.11 0.426 25 33.7 2.3 29.1 2.0 29.7 1.78 0.665 1.56 0.692 32 42.4 2.6 37.2 2.3 37.8 2.55 1.09 2.27 1.12 40 48.3 2.6 43.1 2.3 43.7 2.93 1.46 2.61 1.50 50 60.3 2.9 54.5 2.3 55.7 4.11 2.33 3.29 2.44 65 76.1 2.9 70.3 2.6 70.9 4.71 3.88 5.24 3.95 80 88.9 3.2 82.5 2.9 83.1 6.76 5.34 6.15 5.42 100 114.3 3.6 107.1 3.2 107.9 9.83 9.00 8.77 9.14 125 139.7 4.0 131.7 3.6 132.5 13.4 13.6 12.1 13.8 150 168.3 4.5 159.3 4.0 160.3 18.2 19.9 16.2 20.2 200 219.1 6.3 206.5 4.5 210.1 33.1 33.5 23.8 34.7 250 273.0 6.3 260.4 5.0 263.0 41.4 53.2 33.0 54.3 300 323.9 7.1 309.7 5.6 312.7 55.5 75.3 44.0 76.8 350 355.6 8.0 339.6 5.6 344.4 68.6 90.5 48.3 93.1 400 406.4 8.8 388.8 6.3 393.8 86.3 118.7 62.2 121.7 500 508.0 11.0 486.0 6.3 495.4 135 185.4 77.9 192.7 600 610.0 12.5 585.0 6.3 597.4 184 268.6 93.8 280.2 * above nominal diameter DN 32 identical to DIN 2448
20
** above nominal diameter DN 25 identical to DIN 2458
3
Head Loss in Straight Pipes
mm 15
25
20
32
40
S
12 5
70 0 80 0 90 10 0 00
60 0
50 0
80 10 0
15 0 17 5 20 0
65
2E
50
12 00 14 00 16 0 d = 180 0 20 0 00 mm
3PECIFICHEADLOSS(,
M
30 0 35 0 40 0
25 0
d=
V
M M
.EWUNTREATEDSTEELPIPE
&LOWRATE1
MH
LS
Fig. 11: Head losses HL for new steel pipes (k = 0.05 mm) (enlarged view on p. 82)
0LASTICPIPEANDDRAWNMETALTUBING
M M
Temperature factor J
D
3PECIFICHEADLOSS(,
D M
M
S
M
2E
V
M M
# Temperature t
HL correction for plastic pipe
&LOWRATE1
MH LS
Fig. 12: Head losses HL for hydraulically smooth pipes (k = 0) (enlarged view on p. 83). For plastic pipe when t = 10 °C multiply by the temperature factor j.
21
3
Head Loss in Straight Pipes · Valves and Fittings
The head losses HL in plastic (for example PE or PVC) pipes or smooth drawn metal pip ing are very low thanks to the smooth pipe surface. They are shown in Fig. 12 and valid for water at 10 °C. At other tem peratures, the loss for plastic pipes must be multiplied with a temperature correction factor
indicated in Fig. 12 to account for their large thermal expan sion. For sewage or other un treated water, an additional 20 – 30% head loss should be taken into consideration for po tential deposits (see section 3.6).
3.2.1.2.2 Head Loss in Valves and Fittings The head loss in valves and fit tings is given by HL = ζ · v2/2g
(15)
where ζ Loss coefficient v Flow velocity in a charac teristic crosssection A (for example the flange) in m/s g Gravitational constant 9.81 m/s2 Tables 5 to 8 and Figures 13 to 15 contain information about the various loss coefficients ζ for valves and fittings for operation with cold water.
1 2 3
6
7
8
4
5
9 10
11 12 13 14 15
16 17 18 19 Fig. 13: Schematic representation of the valve designs listed in Table 5
22
The minimum and maximum in Table 5 bracket the values given in the most important technical literature and apply to valves which have a steady ap proach flow and which are fully open. The losses attributable to straightening of the flow dis turbances over a length of pipe equivalent to 12 x DN down stream of the valve are included in the ζ value in accordance with VDI/VDE 2173 guidelines. Depending on the inlet and exit flow conditions, the valve models used and the develop ment objectives (i.e. inexpensive vs. energysaving valves), the loss values can vary dramatically.
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3
23
3
Head Loss in Valves and Fittings · Loss Coefficients for Fittings
Table 6: Loss coefficients ζ in elbows and bends ,Õ`ÊiLÜ
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Pressure loss in Pa Loss coefficient Density in kg/m3 Flow velocity in m/s
and the reversible pressure change of the frictionless flow according to Bernoulli’s equa tion (see 3.2.1.1):
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«iÃ>ÌÊÌÕLiÊLi`Ê ZÊzÊä°ÈÊÌÊä°n
Ài>Ãi`ÊV«iÃ>ÌÊÌÕLiÊLi`Ê ZÊzÊ£°ÎÊÌÊ£°È iÜÃÌÞ«iÊV«iÃ>ÌÊÌÕLiÊLi`Ê ZÊzÊÎ°ÓÊÌÊ{ iÌÊ««iÊvÌÌ}Ã\
For accelerated flows (for ex ample a reduction in the pipe diameter), p2 – p1 is always negative, for decelerated flows (e.g. pipe expansion) it is always positive. When calculating the net pressure change as the arith metic sum of pL and p2 – p1, the pressure losses from Eq. 16 are always to be subtracted. Often the socalled kv value is used instead of the loss coef
24
D
p2 – p1 = · (v12– v22)/2 (17)
iÌÊi`}i 
>À«Ê
>viÀi`Ê
ZÊzÊ ZÊzÊ
ä°xÊ ä°ÓxÊ
ÎÊ ä°xxÊ
Ê ä°ÓäÊ
Ê ä°äxÊ
vÀÊ DÊrÊÇxcÊ ÈäcÊ {xc Ê ZÊzÊä°ÈÊ ä°ÇÊ ä°n
ÃV
>À}iÊ««iÊvÌÌ}Ã\ ZÊzÊ£Ê `ÜÃÌÀi>ÊvÊ>Ê>`iµÕ>ÌiÊi}Ì
ÊvÊÃÌÀ>}
ÌÊ««iÊÜÌ
Ê>Ê>««ÀÝ Ê >ÌiÞÊÕvÀÊÛiVÌÞÊ`ÃÌÀLÕÌÊÊÌ
iÊÕÌiÌÊVÀÃÃÃiVÌ ZÊzÊÓÊ vÀÊ>ÊÛiÀÞÊÀÀi}Õ>ÀÊÛiVÌÞÊ`ÃÌÀLÕÌ]ÊvÀÊiÝ>«iÊi`>ÌiÞÊ Ê `ÜÃÌÀi>ÊvÊ>Ê««iÊvÌÌ}ÊÀÊ>ÊÛ>Ûi]ÊiÌV°
ÌÕi`ÊÊiÝÌÊ«>}i
3
Head Loss in Valves and Fittings · Loss Coefficients for Fittings and Flow Meters
Table 8: Loss coefficients ζ for adapters Expansion v
d
Type
Contraction v
D
ficient ζ when calculating the pressure loss for water in valves:
α
d
I
v
D
II
v
d
D
D
III
Type
d/D
0.5
0.6
I α = 8 ° II for α = 15 ° α = 20 ° III IV for 20 ° < α < 40 °
ζ ≈ ζ ≈ ζ ≈ ζ ≈ ζ ≈ ζ ≈
0.56 0.41 0.07 0.05 0.15 0.11 0.23 0.17 4.80 2.01 0.21 0.10
α
d
IV 0.7
0.8
0.9
0.26 0.03 0.07 0.11 0.88 0.05
0.13 0.02 0.03 0.05 0.34 0.02
0.04 0.01 0.01 0.02 0.11 0.01
Table 7 (continued) Flow meters: Short Venturi tube α = 30° v
D
d
α
v
D d
ζ is referred to the velocity v at diameter D. 0.40 0.16
0.50 0.25
Short Venturi tube ζ ≈ 21 Standard orifice ζ ≈ 300
6 2 0.7 85 30 12
The kv value is the flow rate in m3/h which would result from a pressure drop of 1 bar through the valve for cold water. It cor relates with the pressure loss pL in bar with the flow rate Q in m3/h. The notation kvs is used for a fully open valve.
ζ ≈ 16 · d4/kv2
D
Diameter ratio d/D = 0.30 Area ratio m = (d/D)2 = 0.09
where Q Volume rate of flow in m3/h (!) Density of water in kg/m3 pL Pressure loss in bar (!)
Conversion for cold water:
Standard orifice
D
pL = (Q / kv)2 . /1000 (18)
0.60 0.36
0.70 0.49
0.80 0.64
(19)
where d Reference (nominal) diameter of the valve in cm (!)
0.3 0.2 4.5 2
Water meters (volume meters) ζ ≈ 10 For domestic water meters, a max. pressure drop of 1 bar is specified for the rated load. In practice, the actual pressure loss is seldom higher. Branch fittings (of equal diameter)
Qa/Q = 0.2 0.4 Qd
Q
Qd
Q
ζa ≈ – 0.4 0.08 ζd ≈ 0.17 0.30
0.47 0.72 0.41 0.51
Qd
ζa ≈ 0.88 0.89 ζd ≈ – 0.08 – 0.05
0.95 1.10 1.28 0.07 0.21 –
Q
ζa ≈ – 0.38 0 ζd ≈ 0.17 0.19
0.22 0.37 0.09 – 0.17
0.37 –
Qd
ζa ≈ 0.68 0.50 ζd ≈ – 0.06 – 0.04
0.38 0.35 0.07 0.20
0.48 –
Qa
Q Qa 45° Qa 45° Qa
0.6 0.8 1
,OSSCOEFFICIENTZ
Note: The loss coefficients ζa for the branchedoff flow Qa or ζd for the main flow Qd = Q – Qa refer to the velocity of the total flow Q in the branch. On the basis of this definition, ζa or ζd may have negative values; in this case, they are indicative of a pressure gain instead of a pressure loss. This is not to be confused with the reversible pressure changes according to Bernoulli’s equa tion (see notes to Tables 7 and 8).
A
2+
2ADIUSONOUTERCORNER
0.91 –
2+ A
7ITHTURNING VANECASCADE
2ADIUSONINNERCORNER
%LBOWRADIUS2+ $UCTWIDTHA
Fig. 14: Effect of rounding off the inner and outer side of elbows in square ducts on the loss coefficient ζ
25
3
Head Loss in Valves · System Characteristic Curve
,OSSCOEFFICIENTZ
V
J
10
V
V
J
Y
J 2ELATIVEOPENINGANGLEJnJ J
3.2.2 System Characteristic Curve
A
Degree of opening y/a or relative lift y/DN
Fig. 15: Loss coefficients ζ of butterfly valves, globe valves and gate valves as a function of the opening angle or degree of opening (The numbers designate the types illustrated in Fig. 13)
Fig. 16: System characteristic curve Hsys with static and dynamic components
The static component consists of the geodetic head Hgeo and the pressure head difference (pape)/( · g) between the inlet 3
One must be careful to distinguish between this use of “static” and “dynamic” components and the pre cisely defined “static head” and “dy namic head” used in fluid dynamics, since the “dynamic component” of the system head curve consists of both “static head” (i.e. pressure losses) and “dynamic head” (i.e. velocity or kinetic energy head).
26
3YSTEMHEAD(SYS
The system characteristic curve plots the head Hsys required by the system as a function of the flow rate Q. It is composed of the socalled “static” and “dynamic” components (see Fig. 16)3. 3YSTEMHEADCHARACTERISTIC(SYS $YNAMICCOMPONENT(,
VAnVE G
3TATICCOMPONENT(GEO
PAnPE qG
&LOWRATE1
3
System Characteristic Curve · Selection Chart
n
n
n
n
n
n
n
n
n
n
n
n
n n
n
n
n
n
n
n
n n
n n
n
n
n
( M
1MH
1LS
Fig. 17: Selection chart for a volute casing pump series for n = 2900 rpm (First number = nominal diameter of the discharge nozzle, second number = nominal impeller diameter)
and outlet tanks, which are in dependent of the flow rate. The pressure head difference is zero when both tanks are open to the atmosphere. The dynamic component con sists of the head loss HL, which increases as the square of the flow rate Q (see section 3.2.1.2), and of the change in velocity head (va2ve2)/2g between the inlet and outlet crosssections of the system. Two points are suffi cient to calculate this parabola, one at Q = 0 and one at any point Q > 0. For pipe systems connected one after the other (series con nection) the individual system curves Hsys1, Hsys2 etc. are plotted as functions of Q, and
the heads for each flow rate are added to obtain the total system curve Hsys = f(Q). For branched piping systems the system curves Hsys1, Hsys2, etc. of the individual branches be tween the flow dividers are each calculated as functions of Q. The flow rates Q1, Q2, etc. of all branches in parallel for each given head Hsys are then added to determine the total system curve Hsys = f(Q) for all the branches together. The sections before and after the flow dividers must be added as for a series connection.
27
3
Hydraulic Aspects of Pump Selection
3.3 Pump Selection
M
3.3.1 Hydraulic Aspects
(EAD
H
)MPELLER
MM
MH
,S
.03(
M
K7
0OWER
Fig. 18: Complete characteristics of a centrifugal pump
MH
&LOWRATE
100
10 9 H 8 7 m 6 50 5 40 4
7 6 5
10 9 8 7 6 5 4
3
20
The data required for selecting a pump size, i.e. the flow rate Q and the head H of the desired operating point are assumed to be known from the system characteristic curve; the electric mains frequency is also given. With these values it is possible to choose the pump size, the speed of rotation and, if neces sary, the number of stages, from the selection chart in the sales literature (see Figs. 17 and 19). Further details of the chosen pump such as the efficiency η, the input power P, the required NPSHr (see section 3.5.4) and the reduced impeller diameter Dr can then be determined from
30
3
2
4
4
3
3
2
2
2 10 Pump size 1 6
1
2 0.3
0.4
0.5
Pump size 2
3
4 1
5
Pump size 3
Fig. 19: Selection chart for a multistage pump series for n = 2900 rpm
28
Q m3/h
10 2
Pump size 4
3
4
20 5
30 Q l/s
3
Hydraulic Aspects of Pump Selection · Motor Selection
If there are no specific reasons for doing otherwise, a pump should be selected so that the operating point lies near its best efficiency point Qopt (= flow rate at which efficiency is highest, BEP). The limits Qmin and Qmax (for example due to vibration behaviour, noise emis sion as well as radial and axial forces) are given in the product literature or can be determined by inquiry [1]. To conclude the selection, the NPSH conditions must be checked as described in section 3.5. A multistage pump is chosen us ing the same general procedure; its selection chart shows the number of stages in addition to the pump size (Fig. 19). For pumps operating in series (one after the other) the devel oped heads H1, H2, etc. of the individual characteristic curves must be added (after subtracting any head losses which occur be tween them) to obtain the total characteristic H = f(Q). For pumps operating in parallel, the individual characteristics H1, H2, etc. = f(Q) are first reduced by the head losses occurring up to the common node (head loss HL calculation according to sec tion 3.2.1.2) and plotted versus Q. Then the flow rates Q of the reduced characteristics are added to produce the effective characteristic curve of a “vir tual” pump. This characteristic interacts with the system curve Hsys for the rest of the system through the common node.
Drive power relative to pump input power under rated conditions in %
the individual characteristic curve (for example see Fig. 18).
0UMPINPUTPOWERUNDERRATEDCONDITIONS
K7
Fig. 20: Drive power as a function of rated pump input power at the operationg point Example as per ISO 9905, 5199 and 9908 (Class I, II and III) 3.3.2 Mechanical Aspects
3.3.3 Motor Selection
When selecting a pump the me chanical aspects require atten tion in addition to the hydrau lics. Several examples are:
3.3.3.1 Determining Motor Power
– the effects of the maximum discharge pressure and tem perature of the fluid pumped on the operating limits, – the choice of the best shaft sealing method and cooling requirements, – the vibration and noise emis sions, – the choice of the materials of construction to avoid corro sion and wear while keeping in mind their strength and temperature limits. These and other similar re quirements are often specific to certain industries and even to individual customers and must be addressed using the product literature [1] or by consulting the design department.
Operation of a centrifugal pump is subject to deviations from rated speed and fluctuations in the flow volume handled, and, consequently, changes in the operating point (see section 3.4.1). In particular if steep power curves are involved (see Figs. 5 and 6), this may result in a higher required pump input power P than originally speci fied. For practical purposes, a safety allowance is therefore added when the appropriate motor size is selected. Safety allowances may be specified by the purchaser, or laid down in technical codes, see Fig. 20. The safety allowances stipulated by individual associations are shown in the relevant type series literature [1] or the customer’s specification. When energysaving control methods are used (e. g., speed control systems), the maximum
29
3
Motor Selection
If a pump is selected for a product with a density lower than that of water, the motor power required may have to be determined on the basis of the density of water (for example, during the performance test or acceptance test in the test bay). Typical efficiencies h and power factors cos ϕ of standardized IP 54 motors at 50 Hz are shown in Fig. 21, and the curves of ef ficiency h and power factor cos ϕ as a function of relative motor load P/PN in Fig. 22. Table 9 lists types of enclosure that provide protection of elec tric motors against ingress of foreign objects or water, and of persons against accidental contact. The specific heat buildup in both electric motors and flexi ble couplings during startup as well as the risk of premature contactor wear limit the frequen cy of starts. Reference values for the maximum permissible number of starts Z are given in table 10, unless otherwise speci fied. Submersible motor pumps (Figs. 1j to 1m) are readyassembled pump units whose motors need not be selected individually [7]. Their electrical characteristics are given in the type series literature. The motor is filled with air and can be operated submerged in the product han dled thanks to a – in most cases – doubleacting shaft seal with a paraffin oil barrier.
30
Table 9: Types of enclosure for electric motors to EN 60 529 and DIN/VDE 0530, Part 5 The type of protective enclosure is indicated by the IP code as follows: Code letters (International Protection) IP First digit (0 to 6 or X if not applicable) X Second digit (0 to 8 or X if not applicable) X Alternatively letters A, B, C, D and H, M, S, W – for special purposes only. Key to Protection of electrical Protection of persons against digits: equipment against ingress of accidental contact by solid objects First 0 (not protected) (not protected) digit 1 > 50 mm in dia. back of the hand 2 > 12.5 mm in dia. finger 3 > 2.5 mm in dia. tool 4 > 1.0 mm in dia. wire 5 protected against dust (limited wire ingress permitted, no harmful deposits) 6 totally protected against dust wire Protection against ingress of water with harmful consequences Second 0 (not protected) digit 1 vertical dripwater 2 dripwater up to 15° from the vertical 3 sprays (60° from the vertical) 4 sprays (all directions) 5 lowpressure jets of water 6 strong jets of water (heavy sea) 7 temporary flooding 8 permanent flooding
H POLES %FFICIENCYH 0OWERFACTORCOSJ
power peaks which may pos sibly occur must be taken into account.
COSJ
POLES
K7
2ATEDPOWER0.
Fig. 21: Typical efficiencies η and power factors cos ϕ of standardized motors, IP 54 enclosure, at 50 Hz as a function of motor power PN Table 10: Permissible frequency of starts Z per hour for electric motors Motor installation
Dry
Wet (submersible motors)
Motors up to 4 kW 15 30 Motors up to 7.5 kW 15 25 Motors up to 11 kW 12 25 Motors up to 30 kW 12 20 Motors above 30 kW 10 10
3
Motors for Sealless Pumps · Starting Characteristics
K7 H
%FFICIENCYH 0OWERFACTORCOSJ
• The vapour pressure of the fluid pumped must be known, so as to avoid bearing damage caused by dry running when the fluid has evaporated. It is advisable to install monitoring equipment signalling dry run ning conditions, if any.
K7
POLES POLES K7
]
COSJ
2ATEDPOWER00.
K7
Fig. 22: Curve of efficiency η and power factor cos ϕ of standardized IP 54 motors plotted over relative motor power P/PN Submersible borehole pumps, which are mostly used for ex tracting water from wells, are another type of readyassembled units whose motors need not be selected individually (Fig. 1p). On these pumps, the rotor and the windings are immersed in water [7]. Their electrical char acteristics and permissible fre quency of starts are indicated in the type series literature [1].
3.3.3.2 Motors for Sealless Pumps Sealless pumps are frequently used for handling aggressive, toxic, highly volatile or valu able fluids in the chemical and petrochemical industries. They include magneticdrive pumps (Fig. 1f) and canned motor pumps (Figs. 1n and 1o). A magdrive pump is driven by a primary magnetic field rotating outside its flameproof enclosure and running in synchronization with the secondary magnets in side the enclosure [12].
The primary component in turn is coupled to a commercial dry driver. The impeller of a canned motor pump is mounted directly on the motor shaft, so that the rotor is surrounded by the fluid pumped. It is separated from the stator windings by the can [7]. Sealless pump sets are generally selected with the help of compu terized selection programs, tak ing into account the following considerations: • The rotor is surrounded by the fluid pumped, whose kine matic viscosity υ (see section 4.1) must be known, as it influences friction losses and therefore the motor power required. • Metal cans or containment shrouds (for example made of 2.4610) cause eddy current losses, resulting in an increase in the motor power required. Nonmetal shrouds in magdrive pumps do not have this effect.
• Data on specific fluid proper ties such as its solids content and any tendency to solidify or polymerize or form incrus tations and deposits, need to be available at the time of se lection. 3.3.3.3 Starting Characteristics The pump torque Tp transmit ted by the shaft coupling is directly related to the power P and speed of rotation n. Dur ing pump startup, this torque follows an almost parabolical curve as a function of the speed of rotation [10], as shown in Fig. 23. The torque provided by the asynchronous motor must, however, be higher so as to enable the rotor to run up to duty speed. Together with the voltage, this motor torque has a direct effect on the motor’s cur rent input, and the latter in turn on heat buildup in the motor windings. The aim, therefore, is to prevent unwanted heat buildup in the motor by limiting the runup period and/or current inrush [2] (see also Table 11).
31
3
Starting Methods
Table 11: Starting methods for asynchronous motors Starting Type of Current Runup method equipment input time (mains load) D. o. l.
Heat build Mechani Hydraulic Cost Recommended Comments up in motor cal loading loading relation motor designs during startup
Contactor 4–8 · IN Approx. High Very high Very high 1 All (mecha 0.5–5 s nical)
Star Contactor 1/3 of d. o. l. Approx. High Very high Very high 1.5–3 delta combi values 3–10 s nation (mecha nical) Reduced voltage
Mostly limited to ≤ 4 kW by energy supply companies
All; canned mo Usually stiputors and sub lated for motors mersible motors > 4 kW by subject to a energy supply major drop in companies speed during switchover
Autotrans 0.49 times Approx. High High High 5–15 All former, the d. o. l. 3–10 s mostly values 70% tap ping
No currentless phase during switchover (gradually replaced by soft starters)
Soft Soft starter Continuous Approx. High Low Low 5–15 All start (power ly variable; 10–20 s electro typically nics) 3 · IN
Runup and rundown continuously variable via ramps for each individual load appllication; no hydraulic surges
Fre Frequency 1 · IN 0–60 s Low Low Low Approx. All quency inverter 30 inverter (power electro nics)
Too expensive to use solely for runup and rundown purposes; better suited for openor closedloop control
In the case of d.o.l. starting (where the full mains voltage is instantly applied to the mo tor once it is switched on), the full starting torque is instantly available and the unit runs up to its duty speed in a very short period of time. For the motor itself, this is the most favour able starting method. But at up to 4 – 8 times the rated current, the starting current of the d.o.l. method places a high load on the electricity supply mains, particularly if large motors are involved, and may cause prob lematic voltage drops in electri cal equipment in their vicinity. For motor operation on public
32
lowvoltage grids (380 V), the regulations laid down by the en ergy supply companies for d.o.l. starting of motors of 5.5 kW and above must be complied with. If the grid is not suitable for d.o.l starting, the motor can be started up with reduced volt ages, using one of the following methods: Stardelta starting is the most frequent, since most inexpen sive, way of reducing the start ing current. During normal operation, the motor runs in delta, so that the full mains voltage (for example 400 V) is applied to the motor windings.
For startup, however, the wind ings are starconnected, so that the voltage at the windings is reduced by a factor of 0.58 rela tive to the mains voltage. This reduces the starting current and torque to one third of the values of d.o.l. starting, resulting in a longer startup process. The motor runs up in star con nection beyond pullout torque up to the maximum speed of rotation at point B’ in Fig. 23. Then, switchover to delta is ef fected and the motor continues to accelerate up to rated speed. During the switchover period of approx. 0.1 s, the current sup ply to the motor is interrupted
3
Starting Methods
and the speed drops. On pump sets with a low moment of in ertia (canned motors and sub mersible motors), this speed re duction may be so pronounced that switchover to delta may result in almost the full starting current being applied after all, same as with d.o.l. starting.
An autotransformer also serves to reduce voltage at the motor windings and – unlike stardelta starting – allows selection of the actual voltage reduction. A 70% tapping of the transformer, for instance, will bring down the startup torque and current supplied by the mains to 49%
)
#URRENT)
$gg
$ $g
Soft starters are used for elec tronic continuous variation of the voltage at the motor wind ings in accordance with the dimmer principle. This means that the startup time and start ing current can be freely selected within the motor’s permissible operating limits (heat losses due to slip!). Special constraints re garding the frequency of starts (contrary to Table 10) have to be heeded [1]. Frequency inverters (usually for open or closedloop control) provide a soft starting option without the need for any addi tional equipment. For this pur pose, the output frequency and voltage of the frequency inverter (see section 3.4.3) are increased continuously from a minimum value to the required value, without exceeding the motor’s rated current.
)
of the values for d.o.l. starting. The fact that current supply is never interrupted is another ad vantage of autotransformers.
"gg
4ORQUE4
4
"
"g 4 40
OTORSPEEDN
OFNSYNCHR
Fig. 23: Starting curve for current I and torque T of squirrelcage motors in stardelta connection ( = star connection; Δ = delta connection; P = pump)
33
3
Pump Performance · Operating Point · Throttling
3.4 Pump Performance and Control [4], [6], [8] 3.4.1 Operating Point The operating point of a centri fugal pump, also called its duty point, is given by the intersec tion of the pump characteristic curve (see section 3.1.6) with the system characteristic curve (see section 3.2.2). The flow rate Q and the developed head H are both determined by the intersection. To change the op erating point either the system curve or the pump curve must be changed. A system characteristic curve for pumping water can only be changed • by changing the flow resist ance (for example, by chang ing the setting of a throttling device, by installing an orifice or a bypass line, by rebuilding the piping or by its becoming incrusted) and/or
changing the setting of in stalled preswirl control equipment (see section 3.4.8), • for axial flow (propeller) pumps, by changing the blade pitch setting (see section 3.4.9). Please note: the effect of these measures for changing the char acteristic curve can only be pre dicted for noncavitating opera tion (see section 3.5).
(;=
" 4HROTTLING
3YSTEM CURVE(SYS "
3URPLUSHEAD
0;=
• by changing the speed of rota tion (see section 3.4.3),
34
3YSTEMCURVE(SYS
A pump characteristic curve can be changed
• for pumps with mixed flow impellers, by installing or
0UMPCHARAC TERISTICCURVE
• for pumps with radial impel lers, by changing the impel ler’s outside diameter (see sec tion 3.4.6),
Changing the flow rate Q by operating a throttle valve is the simplest flow control method not only for a single adjustment of the flow rate but also for its continuous control, since it requires the least investment. But it is also the most energy wasting method, since the flow energy is converted irreversibly to heat. Fig. 24 illustrates this process: by intentionally increasing the system resistance (for example by throttling a valve on the
• by changing the static head component (for example, with a different water level or tank pressure).
• by starting or stopping pumps operated in series or parallel (see sections 3.4.4 or 3.4.5),
3.4.2 Flow Control by Throttling
3YSTEMHEAD REQUIREMENT
1;=
0 0OWERSAVED 0
1;=
Fig. 24: Change of the operating point and power saved by throttling a pump whose power curve has a positive slope
3
Orifice Plate · Variable Speed
g
Gravitational constant 9.81 m/s2 ΔH Head difference to be throttled in m
Since the area ratio (dBl/d)2 must be estimated in advance, an iterative calculation is neces sary (plotting the calculated vs. the estimated diameter dBl is recommended so that after two iterations the correct value can be directly interpolated, see example calculation 8.20).
4HROTTLINGCOEFFICIENTF
D"L D
3.4.3 Variable Speed Flow Control
!REARATIOD"LD
Fig. 25: Orifice plate and its throttling coefficient f pump discharge side) the origi nal system curve Hsys1 becomes steeper and transforms into Hsys2. For a constant pump speed, the operating point B1 on the pump characteristic moves to B2 at a lower flow rate. The pump develops a larger head than would be necessary for the system; this surplus head is eliminated in the throttle valve. The hydraulic energy is irrevers ibly converted into heat which is transported away by the flow. This loss is acceptable when the control range is small or when such control is only sel dom needed. The power saved is shown in the lower part of the figure; it is only moderate compared with the large surplus head produced.
The same is principally true of the installation of a fixed, sharpedged orifice plate in the discharge piping, which can be justified for low power or short operating periods. The neces sary hole diameter dBl of the orifice is calculated from the head difference to be throttled ΔH, using the following equa tion: dBl = f ·
Q/ g · ∆H
(20)
where dBl Hole diameter of the orifice in mm f Throttling or pressure drop coefficient acc. to Fig. 25 Q Flow rate in m3/h
At various speeds of rotation n, a centrifugal pump has differ ent characteristic curves, which are related to each other by the affinity laws. If the characteris tics H and P as functions of Q are known for a speed n1, then all points on the characteristic curve for n2 can be calculated by the following equations: Q2 = Q1 . n2/n1
(21)
H2 = H1 · (n2/n1)2
(22)
P2 = P1 · (n2/n1)3
(23)
Eq. (23) is valid only as long as the efficiency η does not de crease as the speed n is reduced. With a change of speed, the op erating point is also shifted (see section 3.4.1). Fig. 26 shows the H/Q curves for several speeds of rotation; each curve has an in tersection with the system char acteristic Hsys1. The operating point B moves along this system curve to smaller flow rates when the speed of rotation is reduced.
35
3
Variable Speed · Parallel Operation
(;= (!
(!
" N
(!STAT
(! (! (EADREQUIRED
N
]
1;=
0;=
N
0 0 0
0
0
Power saved
1;=
Fig. 26: Operation of a variable speed pump for different system characteristic curves Hsys1 and Hsys2 (Power savings ΔP1 and ΔP2 at half load each compared with simple throttling) If the system curve is a parabola through the origin as for Hsys1 in the example, the developed head H according to Eq. (22) is reduced to one fourth its value and the required driving power in Eq. (23) to one eighth its value when the speed is halved. The lower part of Fig. 26 shows the extent of the savings ΔP1 compared with simple throttling. If the system curve is a parabola with a large static head compo nent as for Hsys2, it is possible that the pump characteristic at reduced speed has no intersec
36
be considered when choosing the motor. The expenditure for variable speed drives is not low, but it is amortized quickly for pumps which are used often and which are frequently required to run at reduced flows with small static head component Hsys,stat [8]. This is particularly the case for pumps in heating systems.
tion with it and hence, that no operating point results; the low er speed range is then of no use and could be eliminated. The potential power savings ΔP2 at a given flow rate Q are less than for the system curve Hsys1 as shown in the lower part of the diagram [4]. The improve ment compared with throttling decreases as the static head component Hsys,stat increases (i.e., for a lower dynamic head component Hsys,dyn). Variation of the speed usually means varying the electrical driving frequency, which must
3.4.4 Parallel Operation of Centrifugal Pumps Where one pump is unable to deliver the required flow Q at the operating point, it is possi ble to have two or more pumps working in parallel in the same piping system, each with its own nonreturn valve (Fig. 27). Parallel operation of pumps is easier when their shutoff heads H0 are all equal, which is the case for identical pumps. If the shutoff heads H0 differ, the low est shutoff head marks the point on the common H/Q curve for the minimum flow rate Qmin, below which no parallel opera tion is possible, since the nonreturn valve of the pump with smaller shutoff head will be held shut by the other pump(s). During parallel pumping it must be kept in mind that after stopping one of two identical centrifugal pumps (Fig. 27), the flow rate Qsingle of the re maining pump does not fall to half of Qparallel, but rather increases to more than half. The remaining pump might then immediately run at an operat ing point Bsingle above its design point, which must be considered
3
Parallel Operation
Qparallel < 2 · Qsingle
(
(25)
To compute the characteristic curve for parallel operation see section 3.3.1. Starting or stopping individual pumps operated in parallel does save energy, but it allows only a stepped control of the flow rate. For continuously variable con trol, at least one of the pumps must be fitted with a variable speed drive or a control valve must be installed in the common discharge piping [4]. If centrifugal pumps running at fixed speeds and having un stable characteristics (see Fig. 7 in section 3.1.6) are run in par allel, difficulties can arise when bringing another pump online.
#HARACTERISTICOFPUMP)PUMP)) #HARACTERISTICOF PUMP)ORPUMP)) "PARALLEL 3YSTEMCHARACTERISTIC(SYS
"SINGLE 
1SINGLE
" /PERATINGPOINT (3HUTOFFHEAD
(24)
This effect when starting or stopping one additional pump is more intense when the system curve is steeper or when the pump characteristic is flatter. As long as both pumps I and II are running, the total flow rate Qparallel is the sum of QI and QII, i.e.: Qparallel = QI + QII
(
4OTALDEVELOPEDHEAD(
when checking the NPSH values (see section 3.5) and the drive power (see section 3.1.3). The reason for this behaviour is the parabolic shape of the system characteristic Hsys. For the same reason, the reverse procedure of taking a second identical pump on line does not double the flow rate Qsingle of the pump that was already running, but rather increases the flow rate less than that:
1PARALLEL 1)1))1PARALLEL
1PARALLEL1)1))
&LOWRATE1
Fig. 27: Parallel operation of 2 identical centrifugal pumps with stable characteristic curves The problems occur when the developed head H1 of the pump running is larger than the shut off head (i.e., the developed head at Q = 0) of the pump to be started; the second pump is unable to overcome the pressure on its nonreturn valve (Fig. 28, System curve Hsys1). Pumps
(
with unstable characteristics are not suitable for such a low flow operation. (For a lower system curve Hsys2 they would be per fectly able to operate properly since the developed head H2 of the pump running is lower than the shutoff head H0 of the pump to be started).
(SYS (SYS
( ( (
PUMPS
PUMP
1
Fig. 28: Parallel operation of 2 identical centrifugal pumps with unstable characteristics
37
3
Series Operation · Impeller Diameter Reduction
3.4.5 Series Operation In series operation, the pumps are connected one after the other so that the developed heads can be added for a given flow rate. This means that the discharge pressure of the first pump is the inlet pressure for the second pump, which must be considered for the choice of shaft seal and for the strength of the casing. For this reason multistage pumps are usually used for such applications (ex cept for the hydraulic transport of solids, see section 6). They do not pose these shaft sealing problems. 3.4.6 Turning Down Impellers If the flow rate or developed head of a radial or mixed flow centrifugal pump are to be reduced permanently, the out side diameter D of the impeller should be reduced. The reduc tion should be limited to the value for which the impeller vanes still overlap when viewed radially. The documentation of the pump characteristics (Fig. 18) usually shows curves for several diameters D (in mm). Impellers made from hard ma terials, such as those used for solidshandling pumps, or from stainless steel sheet metal, as well as single vane impellers (Fig. 43) and star or periph eral pump impellers cannot be turned down. (The same is true for underfiling as described in section 3.4.7). For multistage pumps, usually only the vanes
38
but not the shrouds of the im pellers are cut back. It is some times possible to simply remove the impeller and diffuser of one stage of a multistage pump and replace them with a blind stage (two concentric cylindrical cas ings to guide the flow) instead of cutting back the impeller vanes. Impellers with a noncylindrical exit section are either turned down or have only their blades cut back as specified in the characteristic curve litera ture (for example, as shown in Fig. 29). If the impeller diameter only needs to be reduced slightly, a rule of thumb can be applied. An exact calculation cannot be made, since the geometrical sim ilarity of the vane angle and exit width are not preserved when turning down the impeller. The following approximate relation ship exists between Q, H and the impeller diameter D to be found (averaged, if required): (Dt/Dr)2 ≈ Qt/Qr ≈ Ht/Hr (26) where subscript t designates the condition before the reduction
Dr
D1
Dt
Fig. 29: Contour for cutting back the vanes of an impeller with a mixed flow exit
of the impeller outer diameter and index r the condition after the reduction. The required (average) reduced diameter re sults as: Dr ≈ Dt · (Qr/Qt) ≈ Dt · (Hr/Ht) (27) The parameters needed to deter mine the reduced diameter can be found as shown in Fig. 30: in the H/Q curve (linear scales required!) a line is drawn con necting the origin (careful: some scales do not start at zero!) and the new operating point Br . The extension of the line intersects the characteristic curve for full diameter Dt at the point Bt. In this way the values of Q and H with the subscripts t and r can be found, which are used with Eq. (27) to find the desired re duced diameter Dr. The ISO 9906 method is more accurate, but also more involved through the consideration of the average diameter D1 of the impeller leading edge (subscript 1), valid for nq < 79 and for a change of diameter < 5%, as long as the vane angle and the impeller width remain con stant. Thus using the nomen clature of Figs. 29 and 30:
3
Impeller Diameter Reduction · Underfiling · Preswirl · Blade Pitch Adjustment
E q.
28
3.4.8 PreSwirl Control of the Flow
usi ng
$T
g sin
6 .2 Eq
"T u
Total developed head H
(T "R
(R
$R
Flow rate Q
1R
Fig. 30: Determination of the reduced impeller dia meter Dr
1T
(Dr2 – D12)/(Dt2 – D12) = Hr/Ht = (Qr/Qt)2
(28)
A solution is only possible when D1 is known and when a para bola H ~ Q2 is drawn through the reduced operating point Br (with Hr and Qr), not a line as
in Fig. 30, which intersects the base H/Q curve for diameter Dt at a different point Bt (with dif ferent Ht and Qt).
3.4.7 Underfiling of Impeller Vanes
31. The shutoff head does not change. This method is suitable for minor final corrections.
n
3.4.9 Flow Rate Control or Change by Blade Pitch Adjustment The characteristic curves of axial flow (propeller) pumps can be altered by changing the setting of the propeller blade pitch. The setting can be fixed and firmly bolted or a device to change the blade pitch during operation can be used to control the flow rate. The blade pitch angles are
2ELATIVEDEVELOPEDHEAD((OPT
A small, permanent increase of the developed head at the best efficiency point (up to 4 – 6%) can be achieved for radial im pellers by filing the back sides of the backwardcurved vanes, i.e., by sharpening the vanes on the concave side, as shown in Fig.
For tubular casing pumps with mixed flow impellers, the pump characteristic can be influenced by changing the prerotation in the impeller inlet flow. Such preswirl control equipment is often fitted to control the flow rate. The various characteristic curves are then shown in the product literature labelled with the control setting (Fig. 32).
/PERATINGLIMIT
Fig. 31: Underfiled vanes of a radial impeller
HHOPT
0RE SWIRLCONTROLSETTING
2ELATIVEFLOWRATE11OPT
Fig. 32: Characteristic curve set of a centrifugal pump with preswirl control equipment, nq ≈ 160
39
3
Blade Pitch Adjustment · Bypass
shown in the product literature with their respective characteris tic curves (see Fig. 33).
The system characteristic curve can be made steeper by closing a throttle valve, but it can also be made flatter by opening a bypass in the discharge piping as shown in Fig. 34. The pump operating point moves from B1 to a larger flow rate B2. The bypass flow rate is controlled and can be fed back into the inlet tank without being used directly. From the point of view of saving energy, this type of control only makes sense when the power curve falls for in creasing pump flow rates (P1 > P2), which is the case for high specific speeds (mixed and axial flow propeller pumps). For these types of pumps, con trolling the flow by preswirl control or by changing the blade pitch is even more economical, however. The expenditure for a bypass and control valve is not small [4]. This method is also suitable for preventing pumps from operating at unacceptably low flow rates (see operating limits in Figs. 5 and 6c as well as in Figs. 32 and 33).
/PERATINGLIMIT
2ELATIVEDEVELOPEDHEAD((OPT
3.4.10 Flow Control Using a Bypass
HHOPT
"LADEPITCHSETTING
2ELATIVEFLOWRATE11OPT
Fig. 33: Characteristic curve set of an axial flow pump with blade pitch adjustment, nq ≈ 200 (;=
3YSTEMCURVE WITHOUTBYPASS
0UMP CHARACTERISTIC
"
3YSTEMCURVE WITHBYPASS
5SEFULFLOWRATE
"YPASSFLOWRATE "
3URPLUSHEAD

(EADREQUIRED BYTHESYSTEM
1;=
1;=
0;= 0
0OWERSAVED
0
Fig. 34: Characteristic curves and operating points of a pump with a falling power curve and flow control using a bypass. (For a radial flow pump the power curve would increase towards the right and this type of control would cause an increase in power input, see Fig. 5).
40
3
Suction and Inlet Conditions · NPSH Available
e hid
ID E N
TE TRA CH
%TH
%TH A
NO L #A RB O
BAR
"EN Z
EN O 0H OL
OL
0RO PAN
E
4OL U
L
$IE #A THY RBO LE ND THE ISU R LPH IDE
TANE
n
!NI LINE
'LY
CID
CER
IN
MIC ACID
TICA
&OR
!CE TONE "EN ET ZOL HANO L
The NPSHa value is the differ ence between the total pressure in the centre of the pump inlet and the vapour pressure pv, expressed as a head difference in m. It is in certain respects a measure of the probability of vaporization at that location and it is determined only by the operating data of the sys tem and the type of fluid. The vapour pressure of water and other liquids are shown in Table 12 and in Fig. 35 as a function of the temperature.
E !C
o rb Ca OL NZ "E
I "U
The NPSH Value of the System: NPSHa
6APOURPRESSUREP6
3.5.1
AN E
NE TO
LO R
3U LP H UR D N IOX "U IDE TA NE
lp isu nd
!CE
NPSH = Net Positive Suction Head
!M MO N IA
3.5 Suction and Inlet Conditions [3]
4EMPERATURET
#
Fig. 35: Vapour pressure pv of various fluids as a function of the temperature t (for an enlarged view see page 84)
41
3
NPSH Available · Data for Water
Table 12: Vapour pressure pv , density and kinematic viscosity of water at saturation conditions as a function of the temperature t t °C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
pv bar
kg/m3
0.00611 999.8 1.792 0.00656 999.9 0.00705 999.9 0.00757 1000.0 0.00812 1000.0 0.00872 1000.0 0.00935 999.9 0.01001 999.9 0.01072 999.8 0.01146 999.7 0.01227 999.6 1.307 0.01311 0.01401 0.01496 0.01597 0.01703 0.01816 0.01936 0.02062 0.02196 0.02337
999.5 999.4 999.3 999.2 999.0 998.8 998.7 998.5 998.4 998.2
21 22 23 24 25 26 27 28 29 30
0.02485 0.02642 0.02808 0.02982 0.03167 0.03360 0.03564 0.03779 0.04004 0.04241
997.9 997.7 997.5 997.2 997.0 996.7 996.4 996.1 995.8 995.6
31 32 33 34 35 36 37 38 39 40
0.04491 0.04753 0.05029 0.05318 0.05622 0.05940 0.06274 0.06624 0.06991 0.07375
995.2 994.9 994.6 994.2 993.9 993.5 993.2 992.9 992.6 992.2
41 42 43 44 45 46 47 48 49 50
0.07777 0.08198 0.08639 0.09100 0.09582 0.10085 0.10612 0.11162 0.11736 0.12335
991.8 991.4 991.0 990.6 990.2 989.8 989.3 988.9 988.5 988.0
51 52 53 54 55 56 57 58 59 60
0.12960 0.13613 0.14293 0.15002 0.15741 0.16509 0.17312 0.18146 0.19015 0.19920
987.7 987.2 986.7 986.2 985.7 985.2 984.7 984.3 983.7 983.2
42
t °C
n mm2/s
1.004
0.801
0.658
0.553
0.474
pv bar
kg/m3
61 62 63 64 65 66 67 68 69 70
0.2086 0.2184 0.2285 0.2391 0.2501 0.2614 0.2733 0.2856 0.2983 0.3116
982.6 982.1 981.6 981.1 980.5 980.0 979.4 978.8 978.3 977.7
71 72 73 74 75 76 77 78 79 80
0.3253 0.3396 0.3543 0.3696 0.3855 0.4019 0.4189 0.4365 0.4547 0.4736
977.1 976.6 976.0 975.4 974.8 974.3 973.7 973.0 972.5 971.8
81 82 83 84 85 86 87 88 89 90
0.4931 0.5133 0.5342 0.5557 0.5780 0.6010 0.6249 0.6495 0.6749 0.7011
971.3 970.6 969.9 969.4 968.7 968.1 967.4 966.7 966.0 965.3
91 0.7281 92 0.7561 93 0.7849 94 0.8146 95 0.8452 96 0.8769 97 0.9095 98 0.9430 99 0.9776 100 1.0132
964.7 964.0 963.3 962.6 961.9 961.2 960.4 959.8 959.0 958.3
102 1.0878 104 1.1668 106 1.2504 108 1.3390 110 1.4327
956.8 955.5 954.0 952.6 951.0
112 1.5316 114 1.6361 116 1.7465 118 1.8628 120 1.9854
949.6 948.0 946.4 944.8 943.1
122 2.1144 124 2.2503 126 2.3932 128 2.5434 130 2.7011
941.5 939.8 938.2 936.5 934.8
132 2.8668 134 3.0410 136 3.2224 138 3.4137 140 3.614
933.2 931.4 929.6 927.9 926.1
n mm2/s
0.413
t °C
pv bar
kg/m3
145 150
4.155 4.760
921.7 916.9
155 160
5.433 6.180
912.2 907.4
165 170
7.008 7.920
902.4 897.3
175 8.925 180 10.027
892.1 886.9
185 11.234 190 12.553
881.4 876.0
195 13.989 200 15.550
870.3 864.7
205 17.245 210 19.080
858.7 852.8
215 21.062 220 23.202
846.6 840.3
225 25.504 230 27.979
834.0 827.3
235 30.635 240 33.480
820.6 813.6
245 36.524 250 39.776
806.5 799.2
255 260
43.247 46.944
791.8 784.0
265 270
50.877 55.055
775.9 767.9
275 280
59.487 64.194
759.4 750.7
285 290
69.176 74.452
741.6 732.3
295 300
80.022 85.916
722.7 712.5
305 310
92.133 98.694
701.8 690.6
n mm2/s
0.1890
0.1697
0.1579
0.365
0.326
0.295
0.2460
315 105.61 320 112.90
679.3 667.1
325 120.57 330 128.64
654.0 640.2
340 146.08
609.4
350 165.37
572.4
360 186.74
524.4
370 210.53
448.4
374.2 225.60 326.0 0.2160
Density of sea water = 1030 ÷ 1040 kg/m3
0.1488
0.1420
0.1339
0.1279
0.1249
0.1236
0.1245
0.1260
0.1490
3
NPSHa for Suction Lift Operation
3.5.1.1 NPSHa for Suction Lift Operation For suction lift operation (Fig. 8) the pump is installed above the suctionside water level. The value of NPSHa can be calcu lated from the conditions in the suction tank (index e) as follows (see Fig. 36)
2EFERENCEPLANE
/PENSUMP
#LOSEDTANK
PB PE
PBPE
PV T VE
Sg
(SGEO
PV T VE
Fig. 36: Calculation of the NPSHa for suction lift operation for horizontally or vertically installed pumps
NPSHa = (pe + pb – pv)/( · g) + ve2/2g – HL,s – Hs geo ± s’
(29)
where pe Gauge pressure in suction tank in N/m2 pb Absolute atmospheric pressure in N/m2 (Table 13: consider effect of altitude!) pv Vapour pressure in N/m2 (in Table 12 as absolute pressure!) Density in kg/m3 g Gravitational constant, 9.81 m/s2 ve Flow velocity in the suction tank or sump in m/s HL,s Head loss in the suction piping in m Hs geo Height difference between the fluid level in the suction tank or sump and the centre of the pump inlet in m s’ Height difference between the centre of the pump inlet and the centre of the impeller inlet in m Table 13: Influence of the altitude above mean sea level on the annual average atmospheric pressure and on the corresponding boiling point (1 mbar = 100 Pa) Altitude above mean sea level m
Atmospheric pressure pb mbar
Boiling point °C
0 1013 100 200 989 99 500 955 98 1000 899 97 2000 795 93 4000 616 87 6000 472 81
For cold water and open sump (Fig. 36, on the left) at sea level this equation can be simplified with sufficient accuracy for most practical purposes to NPSHa = 10  HL,s  Hs geo ± s’
(30)
The correction using s’ is only necessary when the centre of the impeller inlet (which is the decisive location for cavitation risk) is not at the same height as the centre of the pump inlet (= reference plane). In Fig. 36, Hs geo must be “lengthened” for the pump on the left by the value s’ (i.e., same sign for Hs geo and s’!). When s’ is unknown, it can usually be estimated with enough accuracy by examining the pump’s outline drawing.
43
3
NPSHa for Suction Head Operation · NPSH Required
/PENSUMP PB PE
For cold water and open tanks (Fig. 37, on the left) at sea level this equation can also be simp lified for all practical purposes to:
#LOSEDTANK PBPE
PV T VE
PV T VE
NPSHa = 10 – HL,s + Hz geo ± s’
(ZGEO
Sg
The comments on s’ as outlined in section 3.5.1.1 apply analog ously.
2EFERENCEPLANE
Fig. 37: Calculation of the NPSHa for suction head operation for horizontally or vertically installed pumps 3.5.1.2 NPSHa for Suction Head Operation For operation with positive inlet pressure (also called “suction
head operation”), the pump is installed below the liquid level. Eqs. (29) and (30) change by replacing Hs geo with +Hz geo and then read:
NPSHa = (pe + pb – pv)/( ·g) + ve2/2g – HL,s + Hz geo ± s’
(31)
where Hz geo Height difference between the fluid level in the inlet tank and the centre of the pump inlet in m
( (NON CAVITATING
&IRSTAPPEARANCEOF CAVITATIONBUBBLES
1CONST NCONST
.03(R
.03(
Fig. 38: Experimental determination of the NPSHr for the criterion ΔH = 0.03 Hnoncavitating
44
(32)
3.5.2 The NPSH Value of the Pump: NPSHr When the inlet pressure drops, cavitation bubbles start to de velop in the pump long before their effects become apparent in the hydraulic performance. One must therefore accept the pres ence of a small amount of cavi tation bubbles in order to oper ate economically. The permis sible amount of cavitation can be defined with certain criteria. Often a head drop of 3% result ing from cavitation is accepted. Fig. 38 shows how this point is identified: At a constant flow rate and constant speed of rota tion, the NPSHa of the test loop is reduced until the pump’s dis charge head has fallen by 3%. Other criteria for the cavitation limit can also be used, such as the increase in sound level due to cavitation, the amount of material erosion or a certain reduction in pump efficiency. To avoid impermissible cavita tion conditions, a minimum NPSH value is required, which is shown (in units of m) in the NPSHr curves below the H/Q
3
NPSH Required · Corrective Measures
characteristics (see Fig. 18). The reference plane is the centre of the impeller inlet (Fig. 39), which can vary by the height s’ from the reference plane of the system, for example for vertical pumps (see Figs. 36 and 37).
0Sg
0Sg
0Sg
So as to avoid exceeding the given cavitation limit, it is nec essary that NPSHa > NPSHr
(33)
Fig. 40 shows this graphically at the intersection of the NPSHa and NPSHr curves. If the NPSH requirement is not fulfilled, the developed head will quickly de crease to the right of the inter section (i.e. at larger flow rates), which produces a “cavitation breakdown curve”. Prolonged operation under these condi tions can damage the pump.
( .03(
0Sg 0Sg
0Sg
Fig. 39: Position of the reference point Ps’ for various impellers 3.5.3 Corrective Measures The numerical values of NPSHa and NPSHr are based on the fixed design geometry of the system and of the pump, which cannot be changed after the fact, and on the particular operating point. It follows that
a subsequent improvement of the NPSHa > NPSHr condi tion in an installed centrifugal pump system is only possible with major design and financial expenditure for the pump or the system. Options include: increasing Hz geo or reducing Hs geo (by mounting the tank at
(1CURVE " (SYS
!
!
.03(A .03(A
.03(R 1
1
1
Fig. 40: “Cavitation breakdown curves” A1 and A2 of the H/Q curve in the case of insufficient NPSHa: An NPSH deficit exists in the singly hatched (case 1) and crosshatched regions (case 2). After increasing NPSHa(1) to NPSHa(2), the pump’s useful operating range is increased from Q1 to Q2 and the operating point B can now be reached.
45
3
NPSH Required · Corrective Measures
does not have an impact on the entire flow range of the pump in question, but only on a certain part of the range (see Fig. 42). The resistance to cavitation ero sion can be increased by choos ing more suitable (and more expensive) materials for the impeller, in particular for larger pump sizes.
)NDUCER
Fig. 41: Sectional drawing of a pump with an inducer (detail)
a higher level or installing the pump at a lower point), mini mizing the pressure losses in the inlet piping HL,s or replacing the pump. In the latter case, using a special lowNPSH suc tionstage impeller or installing
In one special case, the elimina tion of an NPSH problem is quite simple: For closed flow loops (for example in a heating system), the system pressure can simply be increased to improve the NPSHa, as long as the sys tem is designed to cope with the higher pressure.
an inducer (propeller in front of the impeller, Fig. 41) can keep the costs of the improvement within limits (a rebuild of the pump is unavoidable, however). It must be kept in mind that the NPSHr reduction by the inducer
.03(VALUEOFTHEPUMP $EVELOPEDHEAD(OFTHEPUMP
0UMPCHARACTERISTICCURVE
.03(RWITHOUTINDUCER
.03(RWITHINDUCER &LOWRATE1
46
1OPT
Fig. 42: Effect of an inducer on the NPSHr
3
Effect of Entrained Solids · Impeller Types for Pumping Waste Water
3.6 Effect of Entrained Solids If the water to be pumped (for example, domestic waste water, rainwater or mixtures) contains small amounts of entrained solids, special impeller and pump types are used (for ex ample with cleaning covers or special shaft seals) [1]. Fig. 43 shows the most common impeller designs for these types of waste water. For pumping sludge, nonclogging channel impellers can be used up to 3% solids content, single vane impellers up to 5%, free flow impellers up to 7% and worm type impellers for even higher concentrations.
Since single vane impellers can not be turned down to adjust the operating point (see section 3.4.6), this type of pump is often driven using a belt drive (see Fig. 59g). Allowances added to the drive power are not shown in Fig. 20, but rather in the product literature [1], since they depend not only on the drive rating but also on the impeller design and specific speed. For example, for single vane impellers pumping domestic waste water or sewage the following power reserves are recommended:
up to 7.5 kW approx. 30% (1kW) from 11 – 22 kW approx. 20% from 30 – 55 kW approx. 15% above 55 kW approx. 10% When assessing the head losses in the piping (see section 3.2.1.2), adequate allowances have to be added [1]. To avoid blockages in the pipes for waste water with high solids concentrations, a minimum flow velocity of 1.2 m/s in horizon tal pipes and 2 m/s in vertical pumps should be maintained. (Exact values can only be de termined experimentally!). This is of particular importance for variable speed drives [1].
Impeller Types for Pumping Waste Water
geschlossenes Einschaufelrad *) für Abwasser mitshown festen oder langfaserigen Front view without shroud Beimengungen
Fig. 43a: Closed single vane impeller for waste water containing solid or stringy substances
geschlossenes Kanalrad *) für feststoff haltige oder schlammige nicht gasende
Front view shown without shroud Flüssigkeiten ohne langfaserige Bei mengungen
Fig. 43b: Closed nonclogging channel impeller for sludge or nongassing liquids containing solids without stringy components
Freistromrad für Flüssigkeiten mit groben oder langfaserigen Feststoffen und Gas einschlüssen
Fig. 43c: Free flow impeller for fluids with coarse or stringy solids and gas content
Schneckenrad für Abwasser mit groben, festen oder langfaserigen Feststoffen oder für Schlämme mit 5 bis 8% Trockensubstanz
Fig. 43d: Worm type impeller for waste water containing coarse, solid or stringy substances or for sludge with up to 5 to 8% solids content
Fig. 43e: Diagonal impeller for waste water containing solid, stringy or coarse substances
47
4
Pumping Viscous Fluids · Shear Curve
4 Special Issues when Pumping Viscous Fluids 4.1 The Shear Curve
When the shear curve is a straight line going through the origin: (34)
7ALL
Fig. 44: Velocity profile between a plane wall and a moving parallel plate. F = Towing force v0 = Towing speed y0 = Distance to wall ∂v/∂y = Rate of shear
the constant factor of propor tionality η is referred to as the dynamic viscosity with the units Pa s. Fluids with this type of curve (for example water or all mineral oils) are normally vis cous or Newtonian fluids, for which the laws of hydrodynamics apply without restriction. If the shear curve is not a straight line through the origin, the fluid is a nonNewtonian fluid, for which the laws of hydrodynamics apply only in a limited fashion. One must therefore strictly differentiate between these two cases. Since the quotient of dynamic viscosity η and density is often used in fluid dynamic relation
A
B $
$ " .
3 3 TTF
Since the viscosity of the fluid causes a shear stress τ not only at the walls, but rather at every distance from the wall within the fluid, the definition of the rate of shear is generalized as ∂v/∂y (change of velocity per change of distance). Just as for the shear stress τ, it is not the same for all wall distances y. During an experiment, pairs of values τ and ∂v/∂y are measured and can be plotted as a func tion, the socalled shear curve (Fig. 45).
VY
T
The movement requires that the resistance force F be over come, which can be expressed as a shear stress τ = F/A. If the wall distance y0, the velocity v0 or the type of fluid is changed, then the shear stress also changes in proportion to the velocity v0 or inversely propor tional to the distance y0. The two easily identified parameters v0 and y0 are combined to yield the shear gradient v0/y0.
48
&
Y
Viscosity is that property of a fluid by virtue of which it of fers resistance to shear. Fig. 44 shows this process. In a fluid, a plate with a wetted surface area A is moved with speed v0 parallel to a stationary wall at a distance y0.
τ = η · ∂v/∂y
V
0LATE
T"TFH
T.H
uVuY
uV uY
uV uY
0LASTICLIMITTF
uVuY
Fig. 45: Overview of the shear behaviour of viscous fluids a without, b with a plastic shear limit τf N Newtonian, B Bingham, S pseudoplastic, D dilatant fluids
4
Pumping Viscous Fluids
ships it is defined as the kine matic viscosity = η/
(35)
Values required to DIN 51 507 (transformer oils) DIN 51 603 (fuel oils) DIN 51 601 (Diesel fuel) ISO viscosity classification to DIN 51 519
Lubricating oils BC
where Kinematic viscosity in m2/s
MMS
η Dynamic viscosity in Pa s (= kg/sm)
Lubricating oils BB
tor
Mo
L,
c
uli
dra
Hy
sH oil
fu
s
oil
ils ro so L, res , VD p L L m Co C, VC B, VB V V ne rbi Tu s TD oil g tin C era s K frig oil Re hine c ma rating A e sK AN frig oil sL Re hine oil CL c ng i a s t l i a m c o bri ing t Lu sC a c oil bri ng Lu ati ric b Lu M
el
ar
ge
s oil el Fu
oils
er
sel
Die
orm
ls L l oi
L
ls E
l oi
e bil
o
tom
Au
nsf Tra
Fue
Fue
Fig. 46: Conversion between various units of kinematic viscosity
4EMPERATURET
bri
Lu
ils
go
in cat
P
CL
ª#
Fig. 47: Kinematic viscosity of various mineral oils as a function of the temperature (enlarged view on page 85) temperature: at higher tempera tures almost all liquids become “thinner”; their viscosity de creases (Figs. 47 and 48).
DW OO D OL SE TS CO EC ND ON S DS
The dynamic viscosity η can be measured for all liquids using a rotating viscometer to determine the shear curve. A cylinder ro tates with a freely chosen speed in a cylindrical container filled with the liquid in question. The required driving torque is meas ured at various speeds along with the peripheral speed, the size of the wetted area and the distance of the cylinder from the wall.
2E
YB
3A
%N G
LE R
EG RE E
S
$
+INEMATICVISCOSITYN %NGLER 3AYBOLTS 2EDWOODS "ARBEYCMH
P
Lubricating oils BA
s
oil
HL
Independently of the discussion above, viscosity varies with
"A
RB
EY
C
M H
n
s
oil
ar
Ge
ZD B ils r o ils Z de o lin er ZA cy lind ils am cy ro de ste am lin ste ted cy d ea m rh eate tea pe h ds Su uper ate S rhe pe Su
For water at 20°C, ν = 1.00 · 10–6 m2/s. For further numerical values see Table 12. The units centistokes = mm2/s, degrees Engler °E, Saybolt seconds S" (USA) and Redwood seconds R" (UK) are no longer used and can be converted to m2/s using Fig. 46.
S ils
Density in kg/m3 (for numeri cal values see Fig. 48)
o el Fu
+INEMATICVISCOSITYN
n
n n M +INEMATICVISCOSITYNIN S
n
49
4
Newtonian Fluids · Viscosity and Pump Characteristics
t = –100 °C N = 2.01 mm2/s t = –92.5 °C N = 2.35 mm2/s
t = –98.3 –84.2 –72.5 –44.5 °C N = 15.8 7.76 4.99 2.33 mm2/s
RBO
3U
LPH
OND
CA
CID
HLO
RIDE
ISULP
HIDE
MM S
!NILIN
#ARB
TRAC
IC &ORMID AC
URI
NTE
0 HE NO L
#A
t =18.3 50 70 °C N = 11.87 3.32 1.95 mm2/s
ZOL
NE
"EN
"ENZOL
4OLUOL
ACID
%THYL
ALCOHO
N "UTANE
!MM
AC
IA
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M
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ID
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ER
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4EMPERATURET
4.2 Newtonian Fluids 4.2.1 Influence on the Pump Characteristics The characteristic curves of a centrifugal pump (H, η and P as functions of Q) only start to change perceptibly at vis cosities above > 20 · 10–6 m2/s and only need to be corrected with empirical conversion fac tors above this limit. The two
50
!CETIC
!NILINE
OL
U 4OL
$ENSITY
NOL
!CETO
Form ic acid (EAVYWA TER 0HENO L
+INEMATICVISCOSITYN
E
ETHA
NE !CETO
KG DM
most well known methods are that described in the Hydraulic Institute (HI) Standards and that of KSB. Both methods use diagrams containing the conver sion factors which are applied in a similar manner, but differ in that the KSB method not only includes the parameters Q, H and but also the significant influence of the specific speed nq (see section 3.1.5). The HI method (Fig. 49) is based on
Fig. 48: Density and kinematic viscosity ν of various fluids as a function of the temperature t (enlarged view on p. 86)
measurements with nq = 15 to 20 and gives the same numerical results as the KSB method (Fig. 50) in this narrow range. The KSB method is based on measurements with nq from 6.5 to 45 and viscosity up to z = 4000 · 10–6 m2/s. The use of both diagrams is explained with the examples shown in them [9]. The flow rate Q, the total developed head H and the ef
4
#ONVERSIONFACTORSK1KH
Conversion factorkH
Viscosity and Pump Characteristics · Conversion Factors
K(
1 1 1 1
K1
KH
n
n
+I
MH
A NEM
LS
N SITY
O ISC
V
TIC
q
q
n
n
q S n M q
q
( EAD (
&LOWRATE1
Fig. 49: Determination of the conversion factors k using the Hydraulic Institute method. Example shown for Q = 200 m3/h, H = 57.5 m, = 500 ·10–6 m2/s
51
4
Viscosity and Pump Characteristics · Conversion Factors
NQ 7
F(
FH
NQ 7
FH
F(
F1
400
NQ W #URVE.O
#URVE.O
EE
3P
D
200 250 300
M
(EAD(7OPTINM
RP IN
300 200 150 100 80 60 50 40 30 20 15 10 8 6 5 4 3 2 1.5 1
+INEMATICVISCOSITYNZIN MM S
400 500 600 800 1000 1500 2000 2500 3000 4000
1
2
0.3 0.4 0.5
3
4 1
5
10 2
3
20 4
5
30 40 50 MH 100 10
LS 20
200
30 40 50
300 400 500 100
1000 200
2000 3000
300 400 500
1000
5000
10000 2000
&LOWRATE17OPT
Fig. 50: Determination of the conversion factors f using the KSB method. Example shown for Q = 200 m3/h, H = 57.5 m, n = 1450 rpm, = 500 · 10–6 m2/s, n = 2900 rpm, nq = 32.8
52
4
Viscosity and Pump Characteristics · Conversion Factors · Conversion
ficiency η, which are known for a singlestage centrifugal pump operating with water (subscript w), can be converted to the val ues for operation with a viscous medium (subscript z) as follows: Qz = fQ · Qw
(36)
Hz = fH · Hw
(37)
ηz = fη · ηw
(38)
The factors f are designated with k in the HI method; both are shown graphically in Figs. 49 and 50. In Fig. 50 the speed of rotation n of the pump must be considered in the diagram and the specific speed nq of the pump impeller must be known, for example from Fig. 3 or Eq. 3. With these factors the known performance for water can be converted to reflect operation with a viscous fluid. The con version is valid for the range
(OWTO&INDTHE/PERATING0OINT 'IVEN &LOWRATE
1W
MH
4OTALDEVELOPEDHEAD
(W
M
3PEEDOFROTATION
N
MIN
+INEMATICVISCOSITY
NZ
MS
$ENSITY
Z
KGM
'RAVITATIONALCONSTANT
G
MS
#ALCULATION 11OPT
1W FROMTHE PUMPCHA (W RACTERISTIC HW FORPOINTS
At flow rate Q = 0, simply set Hz = Hw and ηz = ηw = 0. A worksheet or spreadsheet calcu lation as shown in Fig. 51 can simplify the conversion. After the power is calculated at the three flow rates (in the flow range according to Eq. 39) using
n
MH
M
n
n
n
1/min
F1 W FROM&IG n
n
F( W
n
n
FH W
n
n
1Z1WqF1 W
MH
(Z
= Hw = Hw ∙ fH, w ∙ 1,03 Hw ∙ fH, w Hw ∙ fH, w
1)
HZHWqFH W
ZqGq(Zq1Z 0Z HZqq
M
K7
2)
)F(ZBECOMESLARGERTHAN(W ITSHOULDBESETTO(W
2)
4HESEAREFOURVALUESONTHE(Z1AND1HZCURVEANDTHREEPOINTSONTHE 10ZCURVE0LOTVERSUS1
0.8 Qopt < Q < 1.2 Qopt (39)
At Q = 0.8 Qopt, Hz = 1.03 · fH · Hw applies (but Hz never is > Hw!).
NQ W FROMSECTION n
A simple calculation can thus be done for three flow rates, with a single exception:
Fig. 51: Spreadsheet for calculating the pump characteristics for a viscous fluid using the KSB method (enlarged view on p. 87)
Pz = z · g · Hz · Qz / 1000 ηz
(40)
where z Density in kg/m3 Qz Flow rate in m3/s g Gravitational constant 9.81 m/s2 Hz Total developed head in m ηz Efficiency between 0 und 1 Pz Power in kW (!)
all the characteristic curves can be plotted over Qz using the 3 or 4 calculated points, as shown in Fig. 52 on page 54. For the inverse problem, i.e. when the operating point for the viscous fluid is known and the values for water are to be found (for example when choosing a suitable pump for the requested operating point), the water val ues are estimated and the solu
53
4
Viscosity and Pump/System Characteristics · NonNewtonian Fluids: Pump Characteristics
(
M
(WOPT (ZOPT
H
1WOPT
1ZOPT
(W
(Z
11OPT MH 1
HWOPT
HW
HZOPT
HZ
0
0Z
0ZOPT
K7
MH 1
0WOPT
0W
MH 1
Fig. 52: Conversion of the pump characteristics for water to that for a viscous fluid tion is approached iteratively using fQ, fH and fη in two (or sometimes three) steps.
4.2.2 Influence on the System Characteristics
For specific speeds above nq ≈ 20 the more realistic KSB method results in smaller power requirements; below this limit the calculated required driving power according to HI is too small [9]!
Since the laws of fluid dynam ics retain their validity for all Newtonian fluids, the equations and diagrams for calculating the pipe friction factor and the loss coefficients for valves and fittings are also applicable to viscous media. One must simply substitute the kinematic viscos
54
ity of the viscous liquid z for the water viscosity w when cal culating the Reynolds number Re = v · d/. This yields a lower Reynolds number, and a larger friction factor λz results from Fig. 10. (Note: the influence of the wall roughness can now often be ignored because of the larger boundary layer thickness in the flow.) All of the pressure losses in the pipes, valves and fittings calculated for water in accordance with section 3.2.1.2 are to be increased by the ratio λz/λw. Fig. 53 is also suitable for general practical use: the dia gram provides a fast way of de termining the pipe friction fac tor λz as a function of the flow rate Q, pipe inside diameter d and kinematic viscosity νz. It must be kept in mind, however, that the coefficient λw for water in this diagram is only valid for hydraulically smooth pipes (i.e. not for roughsurfaced pipes)! The corresponding λw can be used to calculate the ratio λz/λw. Since the static component of the system characteristic curve Hsys (Fig. 16) is not affected by viscosity, the “dynamic” com ponent of the system character istic for water can be redrawn as a steeper parabola for a vis cous fluid. 4.3 NonNewtonian Fluids 4.3.1 Influence on the Pump Characteristics Since the local velocity gradients in all the hydraulic components of a pump are not known, a cal
4
NonNewtonian Fluids · Pump/System Characteristics
4.3.2 Influence on the System Characteristics
H
M
&
MM
0IPEINSIDEDIAMETERD
R
W LO
1
E AT
DIA DE I S N I E P 0I
D TER ME
7A TE
RIN
HY
DR
AU
LIC
ALL
YS
MO
OTH
PI
PE
n
n
0IP ,A EFRI C MI NA TION RFL OW FACTO RL Z
+INEMATICVISCOSITYN
0IPEFRICTIONFACTORLZ 4URBULENTFLOW
n
n
M S
When the shear curves are not straight lines of constant linear viscosity, one must divide them into sections and determine the coefficient (= stiffness number) and the exponent n (= structural number) for each section indi vidually (easiest when plotted on doublelogarithmic scales). Using a special diagram (analo gous to Fig. 10), which shows the pipe friction factors λz as a function of the generalized Reynolds number Ren for vari ous exponents n, the value of λz can be read and the system curve Hsys determined for a par ticular flow rate Q. Since this process is very laborious, in par ticular because of the need for multiple iterations, it cannot be recommended for general use. Just as for the pump character istics, in most cases diagrams with a narrow range of applica tion based on experience with a particular fluid are used to find the head loss HL. The more the application differs from the particular conditions of the dia gram, the more uncertain will the head loss analysis become, so that in such cases the experi ence of the design department must be tapped.
Fig. 53: Finding the pipe friction factor λz for viscous liquids Example: Q = 200 m3/h; d = 210 mm; z = 5 · 10–4 m2/s culation of the influence of nonNewtonian fluids on the pump characteristics is not generally possible. Only for a limited number of special fluids, such as fibre pulp, is a prediction based
on knowledge gained during years of experience with this fluid feasible. The selection of a suitable pump must therefore be done by the design department.
55
5
Pumping Gasladen Fluids
In the centrifugal force field of an impeller, the gas bubbles tend to accumulate in certain lo cations and to disturb the flow there. This effect is reinforced
5 Special Issues when Pumping Gasladen Fluids
(EAD(
Unlike dissolved gases, a nondissolved gas in a liquid (ex pressed as a volume percentage) can change the design para meters, the characteristic curve and the general performance of a centrifugal pump dramatically, as shown in Fig. 54 using a nonclogging impeller pump as an example. The gas content may be caused by the production process itself but also by leaking flanges or valve stems in the suc tion line or from airentraining vortices in an open sump inlet when the water level is too low (see section 7.2).
M 2.8% 4.1%
%FFICIENCYH
• the smaller the impeller inlet diameter is, since the throt tling effect of the gas volume is increased, • the lower the specific speed nq of the pump impeller is, and • the lower the speed of rota tion of the pump is. These effects cannot be cal culated. When significant gas
Q,
5.5% 2.8%
8.3% 9.6%
Q, 2.8% 4.1% 5.5%
2.8%
6.9% 8.3% 9.6%
K7
6.9% 8.3% 9.6%
0%
11%
Q,2.8% 4.1%. 5.5%
0%
11%
6.9%
0OWER0
• the more the pump operates at a reduced flow rate, since the lower velocities exert less carrying force on the gas,
11%
MH 4OTALSUCTION SIDEFLOWRATE1S
5.5%
Fig. 54: Influence of nondissolved air on the operation of a nonclogging impeller pump when pumping pretreated sewage (open threechannel impeller, D = 250 mm, n = 1450 rpm, nq = 37) qair = Gas volume in suction piping as % of the mixture.
56
volumes are expected in the pumpage, the following meas ures can be useful: • A sufficiently large settling tank in the suction line can allow the gas to separate out of the fluid and thus mitigate its disturbing effects. • Pipes which are used to fill an open inlet sump must end below the liquid level so that there is no free fall of water that might entrain air bub bles in the tank. In addition, a baffle can prevent the entry of vortices in the suction piping (see Figs. 64 and 65). • Lowflow operation of the main pump can be prevented by installing a special partload pump. When this pump is only needed occasionally, it is advantageous to use a selfpriming pump (whose ef ficiency is lower, though). • A gas removal line in front of the impeller hub requires a vacuum system, is only of limited use for large gas quan tities and disturbs the normal operation of the pump. • In the pump, open impellers (see Fig. 4) with few vanes are advantageous, as is the instal lation of an inducer (Fig. 41). Without any special precau tions, nonclogging impeller pumps (Fig. 43) can pump up to 3%vol and free flow impel lers up to 6 to 7%vol of gas. • If a large gas content is to be expected under normal oper ating conditions, side channel pumps or waterring pumps (positive displacement prin ciple) operate more reliably.
6
Pumping Solidsladen Fluids · Settling Speed
7ATER T#
WSO;MS=
6.1 Settling Speed
S 2E
6 Special Issues When Pumping Solidsladen Fluids
00 000 00 000 7 60 5
80
Solids (which are heavier than water) are most easiest to pump 0 when their settling speed is low 250 0 3 m 200 kg/ 0 est and their flow velocity high 50 =1 s est. Because of the large number 00 40 of influencing parameters, the 0 0 35 settling speed can only be calcu 0 0 30 lated based on simplifying as sumptions: the settling speed of DS;MM= a single sphere in an unlimited space (subscript 0) results from Fig. 55: Settling speed ws0 of individual spherical particles (spherical force equilibrium as diameter d ) in still water D
s
4 g ds s – f · 3 cD f (41)
ws0 =
where ws0 Settling speed in m/s g Gravitational constant 9.81 m/s ds Diameter of sphere in m cD Resistance coefficient of the sphere dependent on Res s Density of the solid in kg/m3 f Density of the fluid in kg/m3 Res = ws0 · ds/f
(42)
The solids concentration: cT = Qs /(Qs + Qf)
considerably because of the mu tual repulsion of the particles, approximately according to the following empirical relationship
(43)
has a large effect, where
ws = ws0 · (1 – cT)5
cT Flowbased solids concen tration (transport concen tration) Qs Flow rate of the solid in m3/s Qf Flow rate of the fluid in m3/s
(44)
The effect of an irregular par ticle shape cannot be estimated; the shape may differ substan tially from that of a sphere. The effect of the particle size distribution can also hardly be calculated. Fig. 56 shows an example of the distribution of
The solids concentration and the boundary effect of the pipe walls reduce the settling speed
ASSFRACTION
where f Kinematic viscosity of the liquid in Pa s
The settling speed ws0 is shown graphically in Fig. 55.
DS
MM
D
Fig. 56: Example of a particle size distribution
57
6
Pumping Solidsladen Fluids · Pump Characteristics
particle sizes ds plotted logarith mically for the portion which passed through a sieve of a given mesh size. Transported solids are almost always composed of particles of various sizes, so that the size distribution has a more or less distinct Sshape. To sim plify the analysis, it can be as sumed that the particle size for 50% mass fraction, designated d50, is representative of the mixture. This assumption is the most important source of dis parities in the planning phase. After all these assumptions and gross approximations, no exact predictions of the effects of solids on the flow behaviour, the system curve, the total de veloped head and the efficiency of pumps are to be expected. The design and selection of pumps for solids transport must therefore be left to experts who have sufficient experience with similar cases. Even then, ex periments are often necessary to attain a measure of certainty. Only certain general tendencies can be stated. 6.2 Influence on the Pump Characteristics
ds, the concentration cT and the density s of the solids as well as the specific speed nq. The ∆H/H = cT / ψ ·
3
Res · (11.83/nq)3 · (s/f – 1)
(45)
where cT Transport concentration according to Eq. 43 ψ Head coefficient of the pump; here approx. = 1 Res Reynolds number of the solids flow according to Eq. 42 nq Specific speed of the pump according to Eq. 3 s Density of the solid in kg/m3 f Density of the fluid in kg/m3 When conveying solids hydrau lically, the pump characteristic curve needs to be shown as de veloped pressure ∆p versus flow rate Q, not as developed head H, since the average density m of the solids / water mixture (in contrast to pumping clean wa ter) is not constant. As simpli fications, the geodetic head dif ference zs,d between the pump inlet and discharge as well as the velocity head difference (cd2 – cs2)/2 g are ignored, i.e., the static head is set to equal the total head (Hp ≈ H): ∆p = m · g · (H – ∆H) (46)
The solids behave differently under the influence of the cen trifugal force field in an impeller than the carrier fluid (usually water) does. The solids cross the streamlines or collide with and rub against the walls of the flow passages. They thus reduce the head H produced in the impeller by the difference ∆H.
where m Average density of the solids / water mixture given by Eq. 47 in kg/m3 g Gravitational constant 9.81 m/s2 H Total developed head in m ∆H Head reduction according to Eq. 45 in m ∆p Pressure in N/m2 (to convert to bar: 1 bar = 100 000 N/m2)
Experimental data exist on the effects of the particle diameter
The average density of the mix ture is given by
58
empirical relationship for the relative head reduction ∆H/H is approximately
m = cT · s + (1 – cT) · w
(47)
where m Average density in kg/m3 s Density of the solid in kg/m3 w Density of water in kg/m3 cT Transport concentration ac cording to Eq. 43 Since the pressure rise in the pump is the product of the density and the developed head (which is reduced when trans porting solids), two independent influences are at work in Eq. 46: the increased average density due to the presence of the sol ids, and the reduced developed head (H – ∆H). Both changes are caused by the solids concen tration, but they have opposite effects, since the density raises the pressure while the head defi cit decreases it. Therefore, no general prediction can be made as to whether the pump pres sure rise will be higher or lower than the water curve when the solids concentration increases. Heavy, smallgrained solids (for example ores) are likely to
6
Pump Characteristics · System Characteristics · Operating Performance · Stringy, Fibrous Solids
produce an increase, while light, large solids (for example coal) and low specific speeds tend to decrease the pressure. 6.3 Influence on the System Characteristics
$EVELOPEDPRESSURE$P0OFTHEPUMP 0RESSURELOSS$PSYSINTHESYSTEM
When the flow velocity drops, solids tend to settle to the bot tom of horizontal pipe runs and collect on the pipe wall. The flow resistance increases and the free flow passage becomes smaller, so that despite the decreasing flow rate, the flow resistance can actually increase. This results in the unusual shape of the system curves as shown in Fig. 57. The minimum in the curves measured at vari ous concentrations is a sure sign that a solids accumulation is taking place and that the pipes
will soon be clogged. The curve minimum is therefore generally considered to be the lower limit of operation. Exact predictions are only possible with sufficient experience or by experiment. 6.4 Operating Performance Fig. 57 shows the typical be haviour of a centrifugal pump transporting solids through a horizontal pipe: with increasing concentration, the intersection of the pump and system charac teristic curves shifts to ever low er flow rates, so that the lower limit of operation could be ex ceeded. To avoid this, a control system must intervene promptly. Throttle valves would be subject to high wear, however, so only a change of rotational speed remains as a feasible control
/PERATINGLIMIT PSYS
C4! #LEANLIQUID
P0
" "
" C40 #LEANLIQUID
method for the hydraulic trans port of solids. Speed control has an additional advantage: when the head developed by the pump impeller drops as the impeller wears, it is possible to compen sate by merely increasing the speed. In vertical pipes, the settling of the solids poses much greater risk, since the pipe can suddenly become plugged if the flow falls below the minimum required, even if only due to stopping the pump. The high erosion rates when pumping granular solids are the decisive parameter for the design of the pumps used. An example of their typical robust design is shown in Fig. 58. The risk of erosion also limits the permissible operating range to near Qopt. High solids concentrations put constraints on the use of centri fugal pumps; the limit values can only be found by experience. The above considerations should have convinced the reader that the selection of pumps for hydraulic solids transport is risky without a solid base of experience and should be left to experts who do this frequently!
6.5 Stringy, Fibrous Solids " 3TEADY STATEOPERATINGPOINTS &LOWRATE1
Fig. 57: Pressure developed by the pump ∆pP and pressure losses of the system ∆psys for various solids concentrations (concentrations cTsys, cTP) of the flow Q. The developed pressure ∆pP = f(cT) can also increase with increasing concentration cTP for solids with high density (here shown decreasing for 10 and 20%).
If long, stringy solids are present in the flow, problems can oc cur, in particular for axial flow (propeller) pumps, when these materials (plant fibres, plastic sheets and rags for example) are caught on the propeller blade leading edge and accumulate
59
7
Solidsladen Fluids · Operating Performance · Stringy, Fibrous Solids
there. The consequences are an increasing head loss and power input, which continue until the driving motor must be stopped due to overloading. The problem can be solved by slanting the leading edges of the propeller blades backwards by shifting the individual profile planes during blade design, just as for a backswept airfoil. Dur ing operation, the fibres can slide along the blade leading edge until they are shredded in the clearance gap at the outside
Fig. 58: Typical centrifugal pump for the hydraulic transport of solids
diameter of the propeller and flushed out. These selfcleaning blades are called “ECBs” (= ever clean blades) [5]. Untreated municipal sewage often contains textiles which tend to form braids and plug impellers with multiple vanes or other flowdividing devices. Single vane impellers, worm type (screw) impellers, or free flow impellers (see Fig. 43) are the better choice for these ap plications.
Figs. 59 a to o: Typical installation arrangements
a
b
c
f
g
h
k
l
m
60
6
Periphery · Pump Installation Arrangements · Intake Structures · Pump Sump
7 The Periphery 7.1 Pump Installation Arrangements Pump installation arrangements are design features in which pumps of the same type (in general of the same series) may differ. Figures 59 a to o provide typical examples of the most frequent installation arrange ments for horizontal and verti cal centrifugal pumps [1]. The major parameters classify ing the pump installation ar rangement are:
• the position of the shaft, i. e. horizontal or vertical (see Figs. a and b, also i and c or h and f),
• the arrangement of the dis charge nozzle on tubular cas ing pumps (see Figs. k, l, m and n),
• the arrangement of the feet, i. e. underneath or shaft centreline (see Figs. d and e),
• the environment of the pump casing, i. e. dry or wet (see Figs. b and o).
• the mode of installation of the pump set, i. e. with or without foundation (see Figs. b and f),
7.2 Pump Intake Structures
• the arrangement of the drive, i. e. on its own or a common baseplate or flanged to the pump (see Figs. g, a, h and i), • the weight distribution of the pump and drive,
7.2.1 Pump Sump Pump sumps (or suction tanks) are designed to collect liquids and be intermittently drained if the mean inlet flow is smaller than the pump flow rate. The sump or tank size depends on the pump flow rate Q and the permissible frequency of starts Z of the electric motors, see sec tion 3.3.3.1. The useful volume VN of the pump sump is calculated using:
d
e
i
j
n
o
Q – Qin VN = Qin · m (48) Qm · Z where Z Max. permissible frequency of starts per hour Qin Inlet flow in m3/h Qm = (Qon + Qoff) / 2 Qon Flow rate at switchon pressure in m3/h Qoff Flow rate at switchoff pressure in m3/h VN Useful volume of pump sump including potential backwash volume in m3 The maximum frequency of starts occurs when the flow rate Qm is twice the incoming flow Qin. The max. frequency of starts per hour is therefore:
61
7
Periphery · Pump Sump · Suction Piping
Zmax = Qm/4VN
(49)
With dirty liquids, solids must be prevented from being depos ited and collecting in dead zones and on the floor. Walls arranged at a 45°, or better still 60° angle, help prevent this (Fig. 60).
7.2.2 Suction Piping The suction pipe should be as short as possible and run with a gentle ascending slope towards the pump. Where necessary, ec centric suction piping as shown in Fig. 61 should be provided (with a sufficient straight length of pipe upstream of the pump L ≥ d) to prevent the formation of air pockets. If, on account of the site conditions, fitting an elbow immediately upstream of the pump cannot be avoided, an accelerating elbow (Fig. 62) helps to achieve a smooth flow. For the same reason, an elbow with multiple turning vanes (see Fig. 63) is required in front of doubleentry pumps or pumps with mixed flow (or axial flow) impellers unless this is impos sible because of the nature of the medium handled (no stringy, fibrous solids, see 6.5).
45 to 60 °
dE
Suction pipe
0.5 dE
Fig. 60: Inclined sump walls to prevent deposits and accumulation of solids
The suction and inlet pipes in the suction tank or pump sump must be sufficiently wide apart to prevent air from being en trained in the suction pipe; posi tive deflectors (Figs. 64 and 65) should be provided, if required. The mouth of the inlet pipe must always lie below the liquid level, see Fig. 65. If the suction pipe in the tank or pump sump is not submerged adequately because the liquid level is too low, rotation of the medium might cause an airentraining vortex (hollow vor tex) to develop. Starting as a funnelshaped depression at the surface, a tubeshaped air cavity forms within a short period of time, extending from the surface to the suction pipe. This will cause the pump to run very un steadily and the output to de crease. The required minimum submergence (minimum depth
Fig. 61: Eccentric reducer and branch fitting to avoid air pockets
62
Fig. 62: Flowaccelerating elbow upstream of a vertical volute casing pump with high specific speed
Fig. 63: Intake elbow with multiple turning vanes upstream of a doubleentry, horizontal volute casing pump (plan view)
Fig. 64: Installation of a positive deflector in the intake chamber of a submersible motor pump
7
Suction Piping · Minimum Submergence
3UCTIONPIPE ≥ dE
dE
7RONG
vE
B
≥ 6 dE
)NLET PIPE
S
≥ 5.5 dE
3UCTION TANK 0.5 dE dE
S
vE B
DN
0OSITIVEDEFLECTOR
B mm 80 80 100 100 150 150 200 200 200
65 80 100 150 200 250 300 400 500
Fig. 65: Piping arrangement in the suction tank / pump sump to prevent air entrainment Fig. 66: Clearances between wall and suction pipe in the suction tank or pump sump according to relevant German regulations. Smin, as shown in Fig. 67. 2 suction pipes arranged side by side require a distance of ≥ 6 dE.
S
≥ dE
vE B
2.0
30
00
S
1.5
S
20
S
dE
Q
Minimum submergence Smin
00
=1
00
m
80 0
1.0 30 0
0.8
0.6
vs
=3
50 0
3
/h
60 0
0
0
80
0.5
40 0
0m
20
15
s m/
00
15
50
2
10
0
60
40 30
0.4 20
dE
1
15
S
S
S
5
0.
0.3 10
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.8 m 1.0
Inlet diameter dE
Fig. 67: Minimum submergence Smin of horizontal and vertical suction pipes (with and without entry nozzle) required for suction tanks to avoid hollow vortices (to Hydraulic Institute standards)
63
Suction Piping · Airentraining Vortex · Minimum Submergence · Intake Structures
of immersion) is specified in Fig. 67, the minimum clearance be tween suction pipes and walls / sump floor in Fig. 66. (Special measures must be taken for tu bular casing pumps, see 7.2.3). The minimum submergence Smin can be read from Fig. 67 as a function of the intake diameter dE (this is the pipe inside diameter of straight, flangeless pipes) or, where available, the inlet diameter of the entry nozzle and the flow rate Q. It can also be calculated according to the following equation given by the Hydraulic Institute: dE (50) g
Smin = dE + 2.3 · vs · where Smin Minimum submergence in m vs Flow velocity = Q/900 π dE2 in m/s, recommended 1 to 2 m/s but never exceeding 3 m/s Q Flow rate in m3/h g Gravitational constant 9.81 m/s2 dE Inlet diameter of suction pipe or entry nozzle in m
Raft Suction pipe
Fig. 68: Raft to prevent airentraining hollow vortices At flow velocities of 1 m/s, the minimum submergence levels specified by the relevant Ger man regulations agree well with the data given above [13]. Wherever the required mini mum submergence cannot or not always be ensured, meas ures as shown in Figs. 68 and 69 have to be taken to prevent airentraining vortices. Irrespec tive of the aspects mentioned before, it should be checked whether the submergence levels also meet the NPSHa require ments laid down in 3.5.2. Round tanks with tangential inlet pipes are special cases but used frequently. The liquid dis charged via the inlet pipe causes the contents of the tank to ro
tate. For this reason baffles as illustrated in Fig. 70 should be provided. 7.2.3 Intake Structures for Tubular Casing Pumps [1] For tubular casing pumps, the minimum submergence and the design of the intake chamber are of particular importance because impellers with high spe cific speeds react very sensitively to uneven inlet flows and airentraining vortices. Fig. 71 shows the arrangement of suction pipes in intake chambers of tubular casing pumps. Refer to Fig. 72 for the mini mum water level required for open, unlined intake chambers
Radial splitter Axial splitter To pump
Suction pipe
To pump
Axial splitter
Tangential inlet
Radial splitter
Baffle Tangential inlet To pump
Fig. 69: Use of swirl preventers
64
Fig. 70: Use of swirl preventers in cylindrical tanks to ensure smooth flow to pump
7
7
Intake Structures · Priming Devices
Lined or covered intake chambers or Kaplan intake elbows are more expensive, but allow pump operation at lower submergence levels [1]. ds
Irrespective of the aspects mentioned before, it should be checked whether the submer gence levels also meet the NPSHa requirements laid down in 3.5.2.
S dE (0.3 ÷ 0.5) dE
7.2.4 Priming Devices
≥ 0.75 dE (2 ÷ 2.5) dE
Entry cone
≥ 4 dE
Fig. 71: Suction pipe arrangement in intake chambers of tubular casing pumps. Smin as shown in Fig. 72 dE ≈ (1.5 ÷ 1.65) ds 2 suction pipes arranged side by side require a distance of > 3 dE with and without entry cones or calculate it using the following equation: dE Smin = 0.8 dE + 1.38 · vs · g (51)
where Smin Minimum submergence in m vs Flow velocity = Q / 900 π dE2 in m/s Q Flow rate in m3/h g Gravitational constant 9.81 m/s2 dE Inlet diameter of bellmouth in m
Most centrifugal pumps are not selfpriming; i. e. their suction pipes and suctionside cas ings must be deaerated prior to startup unless the impeller is arranged below the liquid level. This often inconvenient procedure can be avoided by installing a foot valve (function ing as a nonreturn valve) at the suction pipe mouth (Fig. 73). Deaerating is then only neces sary prior to commissioning and after a long period of standstill. A closed suction tank (static tank) serves the same purpose, in particular when contami nated liquids are handled (it does, however, increase the flow losses and therefore reduces the NPSHa). The tank is under negative pressure and mounted upstream of the pump suction nozzle (Fig. 74). Prior to com missioning it must be filled with liquid. When the pump is started up, it empties the tank, and the air in the suction or siphon pipe is drawn into the suction tank across the apex un til the liquid to be pumped fol
65
7
Priming Devices · Suction Tank
The suction tank volume VB depends on the suction pipe volume and the suction lift capacity of the pump: π pb VB = ds2 · Ls · pb –gHs 4
1.5
4000 3000 2000
1.0
Minimum submergence Smin
lows. After the pump has been stopped, the tank is refilled with liquid via the discharge pipe either manually or automati cally. The air stored in the tank escapes into the suction pipe.
1500
m
1000 800
0.8
600 500 400
0.7 0.6
300 Q = 200 m3/h
0.5 0.4 60 0.3
5 0. 7
0 0. 5
5
2 0.
50
(52)
where VB Suction tank volume in m3 ds Inside diameter of the airfilled inlet pipe in m Ls Straight length of airfilled piping in m pb Atmospheric pressure in Pa (≈ 1 bar = 100 000 Pa) Density of the liquid han dled in kg/m3 g Gravitational constant 9.81 m/s2 Hs Suction lift of pump in m according to equation
150 /s m 100 1. 5 = VE 80 1. 0
40 30
0.2
20 15
0.15
S dE
10
0.1 0.1
0.2
0.3 0.4 Inlet diameter dE
0.5
0.6
0.8 m 1.0
Fig. 72: Minimum submergence Smin of tubular casing pump suction pipe to avoid hollow vortices
,IQUIDLEVELPRIOR TOSTART UP 3UCTIONTANK
0RIMINGPIPE
6ENTHOLE 3HUT OFFVALVE ,IQUIDLEVELIN OPERATION
(SGEO
.ON RETURNVALVE
3TRAINER #ONNECTBARRIERFLUIDSUPPLYLINE
DS
3UCTIONGATEVALVE WITHWATERCUP
Fig. 73: Foot valve (cup valve) with suction strainer
66
Fig. 74: Suction tank arrangement
7
Suction Tank · Measurement Points
(53)
4 Suction tank volume 0.03 0.05 0.1
where
30 50
1 1.5 2
3
5
10 15 20 30
60 m3
100 200 300 500 1000 l
2
Hs geo Vertical distance between water level and pump ref erence plane for suction lift operation in m, see Fig. 36 HL,s Head loss in the suc tion piping in m (refer to 3.2.1.1).
0.2 0.3 0.5
ng t le
h aig Str th of pip ing Ls ] [m
20 15 10 8 6 5
.5 17 5 . 12 9 7
4 2
As HL,s is in most cases notably smaller than Hs geo, Eq. 53 can be neglected and Hs equated with Hs geo. In this case, Fig. 75 provides a much faster way of finding the required tank size.
3 M ax. suc 0 tio 2 n li 1 ft H 4 3 s [m 6 ] 5 7
Hs = Hs geo + HL,s
3 1
For safety reasons the suction tank volume should be multi plied by a factor of 2 to 2.5, or by a factor of up to 3 in the case of smaller pumping stations. The liquid pressure must never reach its specific vaporization pressure at any point in the sys tem. 7.3 Arrangement of Measurement Points In order to achieve a certain accuracy in pressure and veloc ity measurement, the flow must be smooth and regular at the measuring points. Therefore, undisturbed straight lengths of piping need to be arranged up stream and downstream of the measurement point(s), as shown in Fig. 76 and indicated in Table 14. All pipe components which may impede a straight, parallel and nonswirling flow of liquid are considered a disturbance.
Source
Relevant German regulations (VdS – Association of German
VdS 2092‑S 0.5 1.0 2.5 2.5 ISO 9906 2.0 2.0 5+nq/53 –
600
400 300 200 150 100 80 60 50 40 30 1 Inside diameter of suction pipe
20
mm
Fig. 75: Graph to determine the size of the suction tank. Follow the numbers from 1 to 4 for selection. A safety factor of 3.0 has already been considered in the above diagram (head losses HL,s in the suction piping were neglected). Table 14: Minimum values for undisturbed straight lengths of piping at measurement points in multiples of the pipe diameter D Distance from Undisturbed pump flange pipe length Ud/D As/D Ad/D Us/D Inservice measurement Acceptance test measurement
67
7
Ud
D
D
Ad
Measurement Points · Shaft Couplings
As Us
Fig. 76: Arrangement of pressure measurement points up and downstream of the pump Property Insurance Companies) stipulate pipe lengths in mul tiples of the pipe diameter for inservice measurements, while ISO 9906 specifies pipe lengths for acceptance test measurements. The data from both sources are listed in Table 14.
shafts in perfect alignment, since the smallest degree of misalign ment will cause considerable stress on the coupling and on the adjacent shaft sections.
Flexible couplings to DIN 740 are elastic, slipfree connect ing elements between drive and pump which accommodate axi al, radial and angular misalign ment and damp shock loads. Flexibility is usually achieved by the deformation of damping and rubberelastic spring ele ments whose life is governed to a large extent by the degree of misalignment. Fig. 77 shows two of the most common types of flexible shaft coupling. Fig. 78 shows a spacer coupling between a volute casing pump and drive. It permits removal of the pump rotating assembly without having to dismantle the suction and discharge piping or move the pump casing or drive (back pullout design).
If the required straight pipe lengths cannot be provided, the measuring results are likely to be less accurate. Consequently, pump flanges are not suitable as measurement points. The pressure measuring points should consist of a 6 mm dia meter hole and a weld socket to fit the pressure gauge. Even better still are annular measur ing chambers with four drilled holes spread evenly across the circumference.
Fig. 77: Flexible (left) and highly flexible coupling
7.4 Shaft Couplings In centrifugal pump engineer ing, both rigid and flexible shaft couplings are used. Rigid coupl ings are mainly used to connect
68
Fig. 78: Pump with spacer coupling compared with normal coupling
7
Pump Nozzle Loading · Standards and Codes
missible nozzle loading [1].
7.5 Pump Nozzle Loading
As the loading profile for each pump nozzle is made up of three different forces and moments, it is not possible to specify theo retical nozzle loading limits for all conceivable combinations. Therefore, operators either need to check whether the nozzle loading imposed by the system is still within the pump’s permis sible limits, or have to contend with the considerably reduced general limits specified in sev eral national and international standards and codes (EURO PUMP brochure “Permissible flange forces and moments for centrifugal pumps”, 1986; API 610; ISO 5199).
A centrifugal pump mounted on the foundation should not be used as an anchorage point for connecting the piping. Even if the piping is fitted to the noz zles without transmitting any stresses or strains, forces and moments, summarized as nozzle loading, will develop under actual operating conditions (pressure and temperature) and as a result of the weight of the liquidfilled piping. These cause stresses and deformation in the pump casings, and above all changes in coupling alignment, which, in turn, may affect the pump’s running characteristics, the service life of the flexible elements in the shaft coupling, as well as the bearings and me chanical seals. For this reason limits have been defined for per
Z /UTLET X Y Z X )NLET
Y
AX
M
X MA
& 6
&(
AX
.M
M
& 6
AX
M
AX
M
AX
&
M (
0UMPWEIGHTX
KG
$ISCHARGENOZZLEDIA )MPELLEROUTERDIA
7.6 National and International Standards and Codes A series of national standards and other technical codes have been introduced in Germany since the early sixties which govern the dimensions, manu facture, design, procurement and use of centrifugal pumps. Many of the requirements laid down have been included in European and international standards and codes. Drawn up by both operators and manu facturers, these are now wellestablished in virtually all sec tors of industry using or pro ducing pumps. The most impor tant standards are tabulated in Fig. 80 on page 70.
Permissible moments Mmax at the flange reference plane
0ERMISSIBLEFORCES&( MAXAND&6 MAX
Fig. 79 shows the permissible nozzle loading for singlestage volute casing pumps to ISO 5199 (solid line for pumps on
grouted baseplate, broken line for pumps on nongrouted base plates).
Fig. 79: Permissible moments Mmax at the flange reference plane, as well as permissible forces FH,max (at x,z plane) and FV,max (in y direction) to ISO 1599 for singlestage volute casing pumps made of ferritic cast steel or nodular cast iron at room temperature. Lower numerical values apply to austenitic cast steel, lamellar graphite cast iron or higher temperatures.
69
ISO 3661 End suction centrifugal pumps – Baseplate and installation dimensions
End suction centrifugal pumps; Baseplate and installation dimensions
End suction centrifugal pumps (rating 16 bar); Designation, rated performance, main dimensions
ISO 2858 End suction centrifugal pumps (rating 16 bar) – Designation, rated performance and dimensions
DIN EN 23661
DIN EN 22858
Overall dimensions of centrifugal pumps; Tolerances
Side channel pumps PN 40; Rated performance, main dimensions, designation
End suction centrifugal pumps (rating PN 10); with bearing bracket; Rated performance, main dimensions, designation system
DIN EN 735
DIN EN 734
DIN EN 733
Pump nameplates; General specifications
ISO 3069 End suction centrifugal pumps – Dimensions of cavities for mechanical seals and for soft packing
Mechanical seals – Main dimensions, designation and material codes
DIN 242591 DIN 242991 DIN EN 12756 Pumps; Baseplates for machinery; Dimensions
VDMA 24253 Centrifugal pumps with lined casing (lined pumps); single entry, single stage, with axial inlet; Rated powers, dimensions
Multistage centrifugal pumps; Drainage pumps with heads up to 1000 m at a rated speed of 1500 rpm
DIN 24251
VDMA 24252 Centrifugal pumps with wear plates, PN 10 (wash water pumps), with bearing bracket; Designation, rated powers, dimensions
Dimensional Standards: Pumps and Accessories
ISO 9906 Rotodynamic pumps – Hydraulic performance acceptance tests – Grades 1 and 2
DIN EN ISO 9906 Rotodynamic pumps – Hydraulic performance acceptance test – Grades 1 and 2
ISO 5198 Centrifugal mixed flow and axial pumps – Code for hydraulic performance tests; Precision grade
Centrifugal pumps; Nomenclature and component numbers
DIN EN 24250
EN 12162 Liquid pumps – Safety requirements – Procedure for hydrostatic testing
DIN EN 12723 Liquid pumps – General terms for pumps and installations; Definitions, variables, symbols and units
VDMA 242611 Pumps; Designations based on function and design features; Centrifugal pumps
EN 12639 Liquid pumps and pump units; Noise measurement; Test classes 2 and 3
DIN EN 12639 Liquid pumps and pump units – Noise measurement – Test classes 2 and 3
VDMA 24276 Liquid pumps for chemical plant – Quality specifications for materials and components
EN 1151 Circulators with input powers up to 200 W for heating systems and service water heating systems for domestic use – Requirements, testing, marking
Pumps and pump units for liquids; Materials and product tests
DIN 24273
VDMA 24 279 Centrifugal pumps; Technical requirements; Magnetic drive and canned motor pumps
Fig. 80: National and international standards and codes for centrifugal pumps (last update: 2005)
International Organization for Standardization Techn. Comm. TC 115/ Pumps
ISO
Comité Européen de Normalisation European Standards Coordination Committee TC 197 Pumps
CEN
Mechanical Engineering Standards Committee, Pumps
German Standards Institute
DIN
Pump Committee
German Engineering Federation
VDMA
Scope of Application and Responsibilities
Europe
Federal Republic of Germany
International
70
Worldwide
ISO 9905 Technical specifications for centrifugal pumps – Class I
EN 809 Pumps and pump units for liquids; General safety requirements
Pumps and pump units for liquids; Spare parts; Selection and procurement
DIN 24296
VDMA 24292 Liquid pumps; Operating instructions for pumps and pump units; Structure, check list, wording for safety instructions
ISO 5199 Technical specifications for centrifugal pumps – Class II
DIN ISO 9905 (Class I) DIN ISO 5199 (Class II) DIN ISO 9908 (Class III) Centrifugal pumps; Technical specifications
Codes and Specifications
ISO 9908 Technical specifications for centrifugal pumps – Class III
DIN EN 8061 and 2 Technical specifications for drinking water systems
DIN 19885 Technical specifications for drinking water installations, pressure boosting and reducing systems
DIN 244201 Spare parts lists; General DIN 244202 Spare parts lists; Form and structure of text field
DIN EN 12262 Centrifugal pumps; Technical documentation, terms, scope of supply, quality
DIN EN 120564 Gravity drainage systems inside buildings – Part 4: Sewage lifting units; Layout and dimensioning
DIN 1986 Drainage systems for buildings and premises
API 682 Shaft Sealing Systems for Centrifugal and Rotary Pumps
API 610 Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries
American Petroleum Institute
DIN EN 12050 Sewage lifting units for the disposal of waste water from buildings and premises; Design and testing principles
DIN 1989 Rainwater harvesting systems
7 Standards · Codes · Specifications
8
Calculation Examples
8. Calculation Examples
The consecutive numbers of the calculation examples in this chapter are identical to the num bers of the respective equations
in the text. For example, the ap plication dealt with in exercise 8.3 refers to Equation (3).
8.1 Pressure Differential
Sought: The pressure differen tial between the discharge and suction sides indicated by the pressure gauges.
at the respective nozzle levels to keep the same difference in height. If they are mounted at the same level, zs,d must be set to zero. Refer to paragraph 7.3 and ISO DIS 9906 for the cor rect location of the pressure measurement taps).
Given: A volute casing pump Etanorm 80 – 200 with char acteristic curves as per Fig. 18, speed of rotation n = 2900 rpm, impeller diameter D2 = 219 mm, operating point at the point of best efficiency: Q = 200 m3/h, H = 57.5 m, η = 83.5%, water temperature t = 20 °C, density = 998.2 kg/m3. Nominal nozzle diameters DNd = 80; DNs = 100; inside nozzle dia meter dd = 80 mm, ds = 100 mm [1]. Height difference between suction and discharge nozzles zs,d = 250 mm, Fig. 8.
(Taking zs,d = 250 mm into ac count presupposes that the pres sure gauges are fitted exactly
Flow velocities vd = 4 Q / π dd2 = 4 · (200/3600) / π 0.082 = 11.1 m/s vs = 4 Q / π ds2 = 4 · (200/3600) / π 0.102 = 7.08 m/s. According to Eq. (1) the pressure differential is: ∆p = · g · [H – zs,d – (vd2 – vs2) / 2g] = 998.2 · 9.81 · [57.5 – 0.250 – (11.12 – 7.082)/(2 · 9.81)] = 524 576 Pa = 5.25 bar
8.2 Input Power Given: The data as per exercise 8.1. Sought: The input power P.
According to Eq. (2) the input power is: P = · g · Q · H / η = 998.2 · 9.81 · (200 / 3600) · 57.5 / 0.835 = 37 462 W = 37.5 kW
8.3 Specific Speed
nq = n · Qopt / Hopt3/4 = 2900 · (200/3600) / 57.53/4 = 2900 · 0.236 / 20.88 = 32.8 rpm or = 333 · (n/60) · Qopt / (gHopt)3/4 = 333 · 48.33 · (200/3600) / 9.81 · 57.53/4 = 333 · 48.33 · 0.236 / 115.7 = 32.8 (dimensionless)
Given: The data as per 8.1; the specific speed nq is calculated using Eq. (3)
71
8
Calculation Examples
8.5 Bernoulli‘s Equation Given: A centrifugal pump system as shown in Fig. 8 with tanks B and D, designed for a flow rate of Q = 200 m3/h for pumping water at 20 °C. The dischargeside tank is under a pressure of 4.2 bar (positive pressure), the suction tank is open to atmosphere, ve ≈ 0. The geodetic difference in height is 11.0 m; the welded discharge piping has a nominal diameter of DN 200 (d = 210.1 mm acc. to Table 4). The system head loss is 3.48 m. 8.9 Head Loss in Pipes Given: The data as per 8.1 and: suction pipe DN 200, d = 200.1 mm according to Table 4, length = 6.00 m, average abso lute roughness k = 0.050 mm.
Sought: The system head Hsys. Eq. (5) gives: Hsys = Hgeo + (pa – pe) / ( · g) + (va2 – ve2) / 2g + ∑HL where Density = 998.2 kg/m3 according to Table 12 Pressure in tank B: pa = 4.2 bar = 420 000 Pa Pressure in tank D: pe = 0 (pa – pe) / ( · g) = 420 000/(998.2 · 9.81) = 42.89 m va = 4 Q / (3600 · π · d2) = 4 · 200/(3600 · π · 0.21012) = 1.60 m/s (va2 – ve2)/2g = (1.602 – 0)/(2 · 9.81) = 0.13 m Hgeo = 11.00 m ∑HL = 3.48 m
Hsys =
57.50 m
Sought: The head loss HL according to Fig. 11 or Eq. (9). The diagram in Fig. 11 gives: HL = 1.00 · 6.00/100 = 0.060 m The calculation according to Fig. 10 would be more complex and involved, but also absolutely necessary for other roughness values. Relative roughness d / k = 210.1 / 0.050 = 4202 According to Eq. (11), the Reynolds number is Re = v · d / where = 1.00 · 10–6 m2/s, v = Q / A = (Q/3600) · 4 / (πd2) = (200 / 3600) · 4 / (π · 0.21012) = 1.60 m/s, Re = v · d / = 1.60 · 0.2101 / 10–6 = 3.37 · 105. From Fig. 10, d / k = 4202 → λ = 0.016. Eq. (9) gives HL = λ (L / d) · v2 / 2g = 0.016 · (6.00 / 0.2101) · 1.602 / 2 · 9.81 = 0.060 m
72
8
Calculation Examples
Given: The suction pipe described in 8.9, including a slide disc valve DN 200, a 90° elbow with smooth surface and R = 5 d, a foot valve DN 200 and a reducer DN 200 / DN 100 according to Table 8, type IV with an opening angle of α = 30°.
8.15 Head Loss in Valves and Fittings
Sought: The head losses HL. According to Table 5, the loss coefficient of the slide disc valve is Acc. to Table 6, the loss coefficient of the 90° elbow is Acc. to Table 5, the approx. loss coefficient of the foot valve is Acc. to Table 5, the loss coefficient of the reducer is The total of all loss coefficients is
ζ = 0.20 ζ = 0.10 ζ = 2.0 ζ = 0.21 ∑ ζ = 2.51
Eq. (15) then gives the following head loss: HL = ∑ζ · v2 / 2 g = 2.51 · 1.602 / (2 · 9.81) = 0.328 m
Sought: The inside diameter of the orifice plate dBl.
8.20 Orifice Plate
Eq. (20) gives
Given: The pump described in exercise 8.1 is provided with a welded discharge pipe DN 80, the in side diameter being d = 83.1 mm. The discharge head is to be constantly throttled by DH = 5.00 m.
dBl = f ·
#ALCULATEDDIAMETERD"L;MM=
X
The following is calculated first of all: g · DH =
200 /
9.81 · 5.0 = 5.34 m.
First estimate dBl = 70 mm; (dBl / d)2 = 0.709; f = 12.2; Result: dBl = 12.2 · 5.34 = 65.1 mm Second estimate dBl = 68 mm; (dBl / d)2 = 0.670; f = 12.9; Result: dBl = 12.9 · 5.34 = 68.9 mm Third estimate dBl = 68.4; (dBl / d)2 = 0.679; f = 12.8; Result: dBl = 12.8 · 5.34 = 68.4 mm
(g · DH) with f according to Fig. 25.
As an iterative calculation is necessary, dBl is estimated in the first instance, and this value is compared with the calculated diameter. If the two values differ, the value selected for the second estimate lies between the initially estimated and calculated diameters.
Q/
r ete r m ete dia iam d d ate d m te sti cula E l X Ca
Q/
X
%STIMATEDDIAMETERD"L;MM=
For a faster solution, it is recommended to plot the calculated versus the corresponding estimated diameters in a diagram so that the third estimate already provides the final result in the intersection of con necting line and diagonal, see adjacent diagram.
73
8
Calculation Examples
8.21 Change of Speed
Sought: The data for flow rate Q2, discharge head H2 and driving power P2 after change of speed.
Given: The pump speed as per 8.1 (op erating data with index 1) is to be reduced from n1 = 2900 rpm to n2 = 1450 rpm.
Eq. (21) gives Q2 = Q1 · (n2/n1) = 200 (1450 / 2900) = 100 m3/h Eq. (22) gives H2 = H1 · (n2/n1)2 = 57.5 · (1450 / 2900)2 = 14.4 m Eq. (23) gives P2 = P1 · (n2/n1)3 = 37.5 · (1450 / 2900)3 = 4.69 kW, on the assumption that the efficiency is the same for both speeds.
8.27 Turning Down Impellers
Sought: The reduced diameter Dr and the discharge head Hr at BEP after turning down the impeller (Ht = 57.5 m).
Given: The flow rate of the pump at BEP described in 8.1, i.e. Qt = 200 m3/h, is to be reduced to Qr = 135 m3/h by turning down the original impeller diameter Dt = 219 mm.
Eq. (27) gives
8.29 NPSHa for Suction Lift Operation
Question: Is NPSHa sufficient?
Given: The centrifugal pump system described in exercise 8.5 plus the following data: place of in stallation 500 m above M. S. L.; HL,s (refer to exercises 8.9 and 8.15) = 0.39 m; Hs geo = 3.00 m; ve ≈ 0. The pump described in 8.1 is installed horizontally with an open suction tank, as shown in Fig. 36. According to Fig. 18, the pump’s NPSHr is 5.50 m at a flow rate of Q = 200 m3/h.
74
Dr ≈ Dt ·
(Qr / Qt) = 219 ·
(135 / 200) = 180 mm
Eq. (26) gives Hr ≈ Ht · (Qr / Qt) = 57.5 · 135 / 200 = 38.8 m
According to Eq. (29), NPSHa = (pe + pb – pv)/( · g) + ve2/2g – HL,s – Hs geo ± s’ where Gauge pressure in suction tank pe = 0 Atmospheric pressure pb = 955 mbar = 95 500 Pa acc. to Table 13 Vapour pressure pv = 0.02337 bar = 2337 Pa acc. to Table 12 Density = 998.2 kg/m3 acc. to Table 12 (pe + pb – pv)/( · g) = (0 + 95 500 – 2337) / (998.2 · 9.81) = 9.51 m ve2/2g =0 HL,s = 0.39 m Hs geo = 3.00 m s’ = 0, as the centre of the impeller inlet is at the same height as the centre of the pump inlet. NPSHa = 6.12 m With an NPSHr of 5.50 m, NPSHa is larger than NPSHr in this case and therefore sufficient.
8
Calculation Examples
8.31 NPSHa for Suction Head Operation Given: The pump system de scribed in exercise 8.29 is be op erated in suction head operation with a closed tank as shown in Fig. 37. The system data are as follows: place of installation 500 m above M. S. L.; HL,s (re fer to exercises 8.9 and 8.15) = 0.39 m; Hz geo = 2.00 m; ve ≈ 0. The pump described in 8.1 is installed horizontally with a closed suction tank, as shown in Fig. 37. According to Fig. 18, the pump’s NPSHr is 5.50 m at a flow rate of Q = 200 m3/h.
8.36 Pump Characteristics When Pumping Viscous Fluids Given: A mineral oil with a density of z = 0.897 kg/m3 and a kinematic viscosity of nz = 500 · 106 m2/s is to be pumped by the centrifugal pump de scribed in 8.1; characteristic curves according to Fig. 19.
Question: Is NPSHa sufficient? According to Eq. (31) NPSHa = (pe + pb – pv) / ( · g) + ve2/ 2g – HL,s + Hz geo ± s’ where Gauge pressure in suction tank pe = – 0.40 bar = – 40 000 Pa Atmospheric pressure pb = 955 mbar = 95 500 Pa acc. to Table 13 Vapour pressure pv = 0.02337 bar = 2337 Pa acc. to Table 12 Density = 998.2 kg/m3 acc. to Table 12 (pe + pb – pv) / ( · g) = (– 40 000 + 95 500 – 2337) / (998.2 · 9.81) = 5.43 m 2 ve /2g =0 HL,s = 0.39 m Hz geo = 2.00 m s’ = 0, as the centre of the impeller inlet is at the same height as the centre of the pump inlet. NPSHa = 7.04 m With an NPSHr of 5.50 m, NPSHa is larger than NPSHr in this case and therefore sufficient. Flow rate at BEP Head at BEP Optimum efficiency Power Speed Specific speed (as per exercise 8.3) Kinematic viscosity Density of mineral oil
Qw, opt = 200 m3/h Hw, opt = 57.5 m ηw, opt = 0.835 Pw, opt = 37.5 kW n = 2900 min–1 nq = 32.8 nz = 500 · 10–6 m2/s z = 897 kg/m3
The three conversion factors fQ = 0.84, fH = 0.88, fη = 0.62 are taken from Fig. 51.
Sought: The characteristics for discharge head, efficiency and input power when pumping this viscous fluid, using the spread sheet calculation as per Fig. 51.
The calculation is continued using the table below:
The data for handling water (index w) are required first to find the conversion factors:
Qz = Qw · fQ 0 134.4 168 201.6 m3/h Hz = Hw = 1.03 Hw · fH = Hw · fH = Hw · fH 66.5 56.2 50.6 44.9 m ηz = ηw · fη 0 0.502 0.518 0.499 Pz = z · Hz · Qz / (ηz · 367) ÷ 36.8 40.1 44.3 kW
Q/Qopt
0
0.8 1.0 1.2
Qw 0 160 200 240 refer to Hw 66.5 62.0 57.5 51.0 Fig. 18 ηw 0 0.81 0.835 0.805
m3/h m
To calculate the power Pz, the values for flow rate Qz in m3/h and the density z in kg/m3 are inserted into the equation. These calculated points can be used to plot the characteristic curve for a viscous fluid, cf. Fig. 52 and Fig. 18 (this chart is applicable for handling water with an impeller diameter of 219 mm).
75
8
Calculation Examples
8.45 Head Reduction for Hydrotransport Given: Grit with a density of z = 2700 kg/m3 and an average particle size of ds = 5 mm is to be pumped in cold water (kinematic viscosity nf = 1.00 . 10–6 m2/s) at a concentra tion of cT = 15% with a centri fugal pump (hydraulic data as per 8.1, specific speed nq = 33, head coefficient ψ = 1.0). 8.47 Average Density Given: Hydrotransport as de scribed in exercise 8.45. Sought: The average density m and its effect on the pump discharge pressure; will it rise or fall?
Sought: The head reduction DH/H at H = 57.5 m. According to Fig. 55, the settling speed ws0 of a single sphere under the conditions described above is 0.5 m/s. Thus, the Reynolds number is Res = ws0 · ds / nf = 0.5 · 0.005 / 1.0 · 10 – 6 = 2500. The head reduction is calculated using Eq. (45): DH/H = cT / ψ ·
3
Res · (11.83/nq)3 · (s/f – 1) 3
2500 · (11.83 / 33)3 · (2700 / 1000 – 1)
= (0.15 / 1.0) ·
= 0.15 · 13.6 · 0.0461 · 1.70 = 0.16
DH = 0.16 · 57.5 = 9.2 m Under the above conditions the pump discharge head of Hw, opt = 57.7 m would be reduced by 16%, i.e. 57.5 – 9.2 = 48.3 m. According to Eq. (47) the average density is m = cT · s + (1 – cT) · f where f ≡ w = 998,2 kg/m3 for water at 20 °C m = 0.15 · 2700 + 0.85 · 998.2 = 1253 kg/m3 The pressure differential according to equation (46) Dp = m · g · (H – DH) = 1253 · 9.81 · (57.5 – 9.2) = 593 700 Pa = 5.94 bar This is higher than the discharge pressure for handling water (Dp = 5.25 bar) as per exercise 8.1. Hence, the characteristic curve Dp = f (Q) has increased by 13% for hydrotransport of solids.
8.48 Pump Sump
Sought: The useful volume VN of the pump sump according to equa tion (48) (all flow rates in m3/h):
Given: The pump sump for a pump as per 8.1 with the fol lowing data:
VN = Qin · (Qm – Qin) / (Qm · Z)
Inlet flow Qin = 120 m3/h
where
Flow rate at switchon pressure Qon = 220 m3/h and
Qm = (Qon + Qoff) / 2 = (220 + 150) / 2 = 185 m3/h
Flow rate at switchoff pressure Qoff = 150 m3/h
VN = 120 · (185 – 120) / (185 · 10) = 4.22 m3/h
The maximum permissible number of startups of a pump unit is given in Table 10 (section 3.3.3.1, dry motor with P > 30 kW, in this case Z = 10/h).
76
8
Calculation Examples
8.50 Minimum Submergence
Sought: The minimum submergence Smin in the open suction tanks. The flow velocity vs in the suction pipe inlet is
Given: The vertical unflanged suction pipe according to 8.9 and Fig. 8D, inside pipe diame ter d = dE = 210.1 mm at a flow rate of Q = 200 m3/h.
vs = Q/A = (Q/3600)/(p · dE2/4) = (200 / 3600) · (p · 0.21012/4) = 1.60 m/s Eq. (50) gives the minimum submergence as Smin = dE + 2.3 · vs ·
dE / g
= 0.2101 + 2.3 · 1.60 ·
= 0.75 m.
0.2101 / 9.81
The same result can be obtained faster from the diagram in Fig. 67. Fig. 66 provides the required distance to the wall with > 0.21 m, the channel width with > 1.26 m and the distance to the floor with > 0.150 m.
8.52 Suction Tank Volume
Sought: The volume of the suction tank according to Eq. (52):
Given: A centrifugal pump sys tem, data according to 8.1 and 8.9, including a suction tank as per Fig. 74. The straight length of the airfilled suction pipe DN 200 (inside diameter ds = 210.1 mm according to Table 4) is Ls = 3.00 m, with Hs geo = 2.60 m (= vertical distance between pump reference plane and water level for positive inlet pressure operation). The atmos pheric pressure pb = 989 mbar = 98900 Pa; density of the water at 20° C = 998.2 kg/m3, vapour pressure pv = 2337 Pa.
The suction lift Hs is defined by Eq. (53): Hs = Hs geo + HL,s Given is Hs geo = 2.60 m, the suction pipe head loss HL,s is to be cal culated from HL,s1 and HL,s2 as follows:
VB = (ds2 p /4) · Ls · pb / (pb – · g · Hs)
1) Head loss HL,s of the pipe as per 8.9: HL,s1 = λ · (L / ds) · vs2 / 2g where λ = 0.016 from 8.9 L = Hs geo = 2.6 m (not 3.0 m because the elbow length is taken into account in HL,s2) ds = 0.2101 m. vs = 1.60 m from exercise 8.9. HL,s1 = 0.016 · (2.60 / 0.2101) · 1.602 / (2 · 9.81) = 0.026 m HL,s2 covers the 180° elbow (2 x 90° elbow according to Table 6 as in 8.15) and inlet pipe fittings according to Table 7. Loss coefficient ζ of 180° elbow (factor 1.4) = 1.4 · 0.10
= 0.14
Loss coefficient ζ of inlet pipe fitting (broken inlet edge)
= 0.20
HL,s2 = Sζ · vs2 / 2g = (0.14 + 0.20) · 1.602 / (2 · 9.81) = 0.044 m 3) The total head loss HL,s = Hvs1 + HL,s2 = 0.026 + 0.044 = 0.070 m and therefore Hs = Hs geo + HL,s = 2.60 + 0.07 = 2.67 m The example shows that the head loss HL,s (= 0.070) can be neglect ed for short suction pipes, since Hs geo (2.60 m) is considerably high er. This simplifies the calculation. The volume of the suction tank VB can be calculated using Eq. (52) or can simply be determined using the graphs of Fig. 75 (provided the head loss HL,s is neglected).
77
8
Calculation Examples
VB = (ds2p / 4) · Ls · pb / (pb – gHs) = (0.21012 · p/4) · 3.0 · 98 900 / (98 900 – 998.2 · 9.81 · 2.67) = 0.141 m3 The chosen tank size is 2.8 times the volume of 0.40 m3 (cf. example in Fig. 75). Check The lowest pressure is = pb – gHs The vapour pressure is 0.02337 bar
= 72 828 Pa = 2337 Pa
This means the pressure does not fall below vapour pressure during venting.
78
9
Additional Literature
9. Additional Literature
[1] Product literature (KSB sales literature) [2] KSB Centrifugal Pump Lexicon [3] Cavitation in Centrifugal Pumps. KSB publication No. 0383.051 [4] Gebäudetechnik von KSB. Pumpenregelung und Anlagenau tomation. Planungshinweise. (Building Services Products from KSB. Pump Control and Plant Automation. Planning Informa tion). KSB publication No. 2300.024 (2005) [5] Bernauer J., M. Stark, W. Wittekind: Improvement of Propeller Blades Used for Handling Liquids Containing Fibrous Solids. KSB Technische Berichte 21e (1986), pp. 16 – 21 [6] Bieniek K., Gröning N.: Controlling the Output of Centrifugal Pumps by Means of Electronic Speed Control. KSB Technische Berichte 22e (1987), pp. 16 – 31 [7] Bieniek K.: Submersible Motors and Wet Rotor Motors for Centrifugal Pumps Submerged in the Fluid Handled. KSB Tech nische Berichte 23e (1987), pp. 9 – 17 [8] Holzenberger K., Rau L.: Parameters for the Selection of Energy Conserving Control Options for Centrifugal Pumps. KSB Technische Berichte 24e (1988), pp. 3 – 19 [9] Holzenberger K.: A Comparison of Two Conversion Methods Applied to the Characteristics of Centrifugal Pumps While Pumping Viscous Liquids. KSB Technische Berichte 25e (1988), pp. 45 – 49 [10] Holzenberger K.: How to Determine the Starting Torque Curve of Centrifugal Pumps by Using Characteristic Factors. KSB Technische Berichte 26 (1990), pp. 3 – 13 [11] Kosmowski I., Hergt P.: Förderung gasbeladener Medien mit Hilfe von Normal und Sonderausführungen bei Kreisel pumpen (Pumping Gasladen Fluids by Standard and Special Design Centrifugal Pumps). KSB Technische Berichte 26 (1990), pp. 14 – 19 [12] Schreyer H.: Glandless Chemical Pump with Magnetic Drive. KSB Technische Berichte 24e (1988), pp. 52 – 56
79
10
Specific Speed
10. Technical Annex
Fig. 3: Nomograph to determine the specific speed nq Example: Qopt = 66 m3/h = 18.3 l/s; n = 1450 rpm, Hopt = 17.5 m. Found: nq = 23 (metric units).
80
,AMINAR
2E L
2ECRIT
4URBULENT
RVE
G CU
2EYNOLDSNUMBER2E
,IM ITIN
MO
OTH K
&ULLYROUGHK
LLYS
ULIC A
DRA
(Y
Fig. 10: Pipe friction factor λ as a function of the Reynolds number Re and the relative roughness d/k
0IPEFRICTIONFACTORL
DK
Pipe Friction Factor λ
10
81
mm
d
=1 5
25
20
40
32
0
80
&LOWRATE1
2E
50
65
10
S
M
V
LS
MH
.EWUNTREATEDSTEELPIPE
Fig. 11: Head losses HL for new steel pipes (k = 0.05 mm)
3PECIFICHEADLOSS(,
5
M M
12
15 0 17 5 20 0
50 0
25 0
30 0 35 0 40 0
60 0 70 0 80 0 90 10 0 00
82 12 00 14 00 16 0 d = 180 0 20 0 0 0m m
10 Head Loss in Steel Pipes
D
M M
&LOWRATE1
S
Fig. 12: Head losses HL for hydraulically smooth pipes (k = 0) For plastic pipe when t = 10 °C multiply by the temperature factor j
3PECIFICHEADLOSS(,
M
D
M M
V
2E
M M
LS
MH
# Temperature t
HL correction for plastic pipe
0LASTICPIPEANDDRAWNMETALTUBING
Temperature factor J
Head Loss for Hydraulically Smooth Pipes
10
83
84
ZOL
"EN
n
!N
E
ILIN
ERI N
'LY C
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4OL U OL
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UT AN E
CH LO RI D
TR A
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N "
UR
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!M
TICA
CA CID
&OR MI
NE
!CE
L
HANO
TONE ET
%TH A
!CE
PAN E
0RO
I "U TANE
6APOURPRESSUREP6
10 Vapour Pressures
ide
E !C
4EMPERATURET
Fig. 35: Vapour pressure pv of various fluids as a function of the temperature t NE TO
rb Ca
#
on h ulp dis
N "E
L ZO
10
Kinematic Viscosity
Values required to DIN 51 507 (transformer oils) DIN 51 603 (fuel oils) DIN 51 601 (Diesel fuel) ISO viscosity classification to DIN 51 519
Lubricating oils BC
MMS
Lubricating oils BB
s oil
oil
s
Lubricating oils BA
sS
r oto
oil
ar
Ge
el
Fu
M
ne rbi Tu s TD oil g tin C era ils K g i o fr Re hine c g a m tin A N era ils K g i LA o fr ils Re hine o L c ing sC ma cat oil i r g b in Lu sC cat oil bri g u n i L cat bri Lu
el Fu
pe Su
sM
fue
oil
oils
el ies
er orm
ls L
L
ls E
nsf
l oi
l oi Fue
Tra
Fue
l
ZD B ils ro sZ de r oil lin e ZA cy lind ils am cy ro de m ste a lin ste ted cy ea ted m rh a tea pe he ds Su per ate rhe
s P oil HL ear L, g H e s bil oil s mo lic o t u oil Au or L, dra s y s H re VD L mp L, Co C, VC B, VB V V
Su
+INEMATICVISCOSITYN
bri Lu
cat
ils go
P CL
in
D
4EMPERATURET
ª#
Fig. 47: Kinematic viscosity of various mineral oils as a function of the temperature t
85
10
Density and Kinematic Viscosity
t = –100 °C N = 2.01 mm2/s t = –92.5 °C N = 2.35 mm2/s
t = –98.3 –84.2 –72.5 –44.5 °C N = 15.8 7.76 4.99 2.33 mm2/s
t =18.3 50 70 °C N = 11.87 3.32 1.95 mm2/s
3U
NTE TRAC HLO
LPH
ISULP
!NILIN
OND
#ARB
CA CID
IC &ORMID AC
RIDE
URI
HIDE
MM S
0HENOL
#A RBO
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Form ic acid (EAVYWA TER 0HENO L
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IDE
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Fig. 48: Density and kinematic viscosity ν of various fluids as a function of the temperature t
86
+INEMATICVISCOSITYN
E
ETHA
N !CETO
KG DM
10
Viscous Fluids · Pump Characteristics
(OWTO&INDTHE/PERATING0OINT 'IVEN &LOWRATE
1W
MH
4OTALDEVELOPEDHEAD
(W
M
3PEEDOFROTATION
N
MIN
+INEMATICVISCOSITY
NZ
MS
$ENSITY
Z
KGM
'RAVITATIONALCONSTANT
G
MS
#ALCULATION 11OPT
n
MH
M
n
NQ W FROMSECTION n
n
n
1/min
F1 W FROM&IG n
n
F( W
n
n
FH W
n
n
1Z1WqF1 W
MH
1W FROMTHE PUMPCHA (W RACTERISTIC HW FORPOINTS
(Z
= Hw = Hw ∙ fH, w ∙ 1,03 Hw ∙ fH, w Hw ∙ fH, w
1)
HZHWqFH W
ZqGq(Zq1Z 0Z HZqq
M
K7
2)
)F(ZBECOMESLARGERTHAN(W ITSHOULDBESETTO(W
2)
4HESEAREFOURVALUESONTHE(Z1AND1HZCURVEANDTHREEPOINTSONTHE 10ZCURVE0LOTVERSUS1 Fig. 51: Spreadsheet for calculating the pump characteristics for a viscous fluid using the KSB method
87
88
Velocity head
Velocity head v /2 g as a function of flow rate Q and inside pipe diameter d
2
Flow rate Q
Flow rate Q
10 Velocity Head
Velocity head
Velocity head differential
Velocity head differential ∆ (v2/2 g) as a function of flow rate Q and inside pipe diameters d1 and d2
Flow rate Q
Flow rate Q
Velocity Head
10
89
Velocity head differential
11 11. Excerpt of Important Units for Centrifugal Pumps Physical Sym Units dimension bol SI units Other units (not complete)
Units not Recom to be used mended any longer units
Length l m Metre
km, dm, cm, mm, µm
Volume V m3
dm3, cm3, mm3, litre (1 l = 1 dm3)
m
Base unit
cbm, cdm… m3
m3/h, l/s Flow rate, capac Q, m3/s · ity, volume flow V
l/s and m3/s
Time t s Second
s
Speed of rotation
Comments
s, ms, µs, ns,… min, h, d
Base unit
n 1/s 1 /min (rpm) 1 /s, 1 /min
Mass m kg Kilogram g, mg, µg, Pound, kg metric ton hundred (1 t = 1000 kg) weight
Base unit The mass of a commercial commodity is described as weight.
Density kg/m3 kg/dm3 kg/dm3 und kg/m3
The term “spezifice gravita” must no longer be employed, because it is ambiguous (see DIN 1305).
Mass moment of J inertia · Mass rate of flow m
kg m2
kg m2
kg/s
kg/s and t/s
t/s, t/h, kg/h
Mass moment, 2. order
Force F N Newton kN, mN, µN,… kp, Mp,… N 1 kp = 9.81 N. The weight (= kg m/s2) force is the product of the mass m by the local gravi tational constant g. Pressure p Pa Pascal bar kp/cm2, at, bar 1 at = 0.981 bar (= N/m2) (1 bar=105 Pa) m w.c., = 9.81 · 104 Pa Torr, … 1 mm Hg = 1.333 mbar 1 mm w.c. = 0.098 mbar Mechanical σ, τ Pa stress (strength) Bending mo ment, torque
M, T
Pascal (= N/m2)
N/mm2, N/cm2… kp/cm2,
N m
Energy, work, W, J quantity of heat Q
kp m, …
N/mm2 1 kp/mm2 = 9.81 N/mm2
N m 1 kp m = 9.81 N m
Joule kJ, Ws, kWh, … kp m J und kJ 1 kp m = 9.81 J (= N m 1 kW h = kcal, cal, 1 kcal = 4.1868 kJ = W s) 3600 kJ WE
Total head H m Metre m l. c. m
The total head is the work done in J = N m applied to the mass unit of the fluid pumped, referred to the weight force of this mass unit in N.
Power P W
Watt MW, kW, kp m/s, PS kW 1 kp m/s = 9.81 W (= J/s 1 PS = 736 W = N m/s)
Temperature difference
Kelvin
T
K
°C
°K, deg.
K
Base unit
n m2/s Kinematic viscosity
St (Stokes), m2/s 1 St = 10–4 m2/s °E, … 1 cSt = 1 mm2/s
η Pas Dynamic viscosity
P (Poise)
Pascal second (= N s/m2)
Pa s 1 P = 0.1 Pa s
Qopt Specific speed nq 1 1 nq = 333 · n · (g Hopt)3/4 Sl units (m und s)
90
91
e 46,–
KSB Aktiengesellschaft D67225 Frankenthal (Pfalz) / Germany Telephone +49 6233 860 • Fax +49 6233 863401 • www.ksb.com
92
0101.5/510 / 09.06 / Ottweiler
ISBN 3000178414