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8.4 CHAPTER EIGHT FIGURE 1 Length of system controlled by pump FIGURE 2 Branch-line pumping system FIGURE 3 Pumps in serie... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.5 An incompressible liquid can have energy in the form of velocity, pressure... 8.6 CHAPTER EIGHT FIGURE 4 Equivalent static head FIGURE 5 Liquids of different specific weights (also specific gravities)... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.7 FIGURE 6 The total head, or energy, in foot-pounds per pound (newtonmeters... 8.8 CHAPTER EIGHT FIGURE 7 Centrifugal pump total head the pressure head, or energy, in foot-pounds per pound (newton-mete... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.9 FIGURE 8 Example 1 where the subscripts d and s denote discharge and sucti... 8.10 CHAPTER EIGHT where the subscripts 1 and 2 denote points in the pumping system anyplace upstream and downstream from ... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.11 (a) From Eq. 4, and Eq. 8, in USCS units in SI units Therefore, in USCS u... 8.12 CHAPTER EIGHT FIGURE 9 Energy and hydraulic gradients in SI units ENERGY AND HYDRAULIC GRADIENT _____________________... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.13 FIGURE 10 Construction of system total-head curve pose of selecting a pum... 8.14 CHAPTER EIGHT FIGURE 11 System total-head curve for Example 1 head for the same flow. When a pump is being purchased,... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.15 FIGURE 12 Construction of system total-head curve to determine gravity fl... 8.16 CHAPTER EIGHT FIGURE 14 Varying centrifugal pump speed to maintain constant flow for the different reservoir levels s... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.17 purchasing purposes—for example, primary condensate pump system, secondar... 8.18 CHAPTER EIGHT FIGURE 16A Approximate comparison of head and efficiency versus flow for impellers of different specifi... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.19 FIGURE 17 Variation in head when a centrifugal pump is started with a clo... 8.20 CHAPTER EIGHT FIGURE 21 Variation of torque during start-up of a high-specific-speed pump with a closed valve, an ope... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.21 FIGURE 22 Typical reverse-speed-torque characteristics of a low-specific-... 8.22 CHAPTER EIGHT FIGURE 24 Transient system head as a result of liquid acceleration and system friction when a propeller... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.23 where L length of constant-cross-section conduit, ft (m) V velocity ... 8.24 CHAPTER EIGHT FIGURE 25 Transient total pump torque as a result of liquid acceleration and system friction when a pro... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.25 FIGURE 26 Propeller pump and motor speed-torque curves, showing effect of... 8.26 CHAPTER EIGHT FIGURE 28 Transient system total head priming a siphon (12) where HB barometric pressure head of liqu... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.27 TABLE 1 Values for determining pipe-diameter ratio versus (ft3 /s)/d5/2 i... 8.28 CHAPTER EIGHT FIGURE 29 Area versus depth for a circular pipe In SI units: 1 meter 3.28 feet 1 VD (V in m/s, D in m... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.29 FIGURE 30 Multiple siphon system (Z normal system static head when pipe... 8.30 CHAPTER EIGHT From Eqs. 9 and 12, in USCS units in SI units Because the maximum height is exceeded (Z1 Zs), siphon ... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.31 From Eq. 13 EXAMPLE 3 Calculate the minimum total system head using condi... 8.32 CHAPTER EIGHT From Figure 29, the ratio of the filled area to the area of a full pipe is 0.625 for a depth- to-diamet... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.33 Liquids such as water and mineral oil, which exhibit shear stresses propo... 8.34 CHAPTER EIGHT (16) where f friction factor L pipe length, ft (m) D inside pipe diameter, ft (m) V average pip... 8.35 [[A5655]] FIGURE 31 Moody diagram. (Reference 14) In SI units: ( in kg /m3 , V in m/s, D in m, µ in N • s/m2 .) 1 me... 8.36 CHAPTER EIGHT TABLE 2 Values of friction factor C to be used with the Hazen-Williams formula in Figure 34 Type of pip... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.37 FIGURE 32 Relative roughness and friction factors for new, clean pipes fo... 8.38 CHAPTER EIGHT FIGURE 33 Kinematic viscosity and Reynolds number. (Hydraulic Institute Engineering Data Book, Ref.eren... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.39 In SI units EXAMPLE 7 The flow in Example 6 is increased until complete t... 8.40 CHAPTER EIGHT FIGURE 34 Nomogram for the solution of the the Hazen-Williams formula. Obtain values for C from Table 2... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.41 polation. For pipe sizes not shown, multiply the fourth power of the rati... TABLE 3 Frictional loss for viscous liquids (Hydraulic Institute Engineering Data Book, Reference 5) Pipe Viscosity, SSU g... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.43 LAMINAR FLOW TABLE 3 Continued. Viscosity, SSU 2500 3000 4000 5000 6000 7... TABLE 3 Continued. Pipe Viscosity, SSU gpm size 100 200 300 400 500 1000 1500 2000 3 2.7 3.1 3.2 3.2 4 8 11.9 15.9 120 4 0... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.45 TABLE 3 Continued. Viscosity, SSU 2500 3000 4000 5000 6000 7000 8000 9000... TABLE 3 Continued. Pipe Viscosity, SSU gpm size 20,000 25,000 30,000 40,000 50,000 60,000 2 19.3 24.1 28.9 38.5 48.2 58 3 ... 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.47 TABLE 3 Continued. Viscosity, SSU 70,000 80,000 90,000 100,000 125,000 15... TABLE 3 Continued. Pipe Viscosity, SSU gpm size 20,000 25,000 30,000 40,000 50,000 60,000 6 8.7 10.8 13 17.3 21.7 26 100 8... PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS PUMPS SYSTEMS Upcoming SlideShare Loading in …5 × 1 of 80

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PUMPS SYSTEMS 1. 1. Pump Systems C • H • A • P • T • E • R • 8 2. 2. SECTION 8.1 GENERAL CHARACTERISTICS OF PUMPING SYSTEMS AND SYSTEM-HEAD CURVES J. P. MESSINA 8.3 1 1 bar 15 Pa. 2 Work per unit weight mass, rather than weight force, is sometimes called specific delivery work; it has the units of newton-meters per kilogram and is equal to total head multiplied by g, the gravitation constant. SYSTEM CHARACTERISTICS AND PUMP HEAD___________________________ A pump is used to deliver a specified rate of flow through a particular system.When a pump is to be purchased, this required capacity must be specified along with the total head neces- sary to overcome resistance flow and to meet the pressure requirements of the system com- ponents. The total head rating of a centrifugal pump is usually measured in feet (meters), and the differential pressure rating of a positive displacement pump is usually measured in pounds per square inch (kilopascals or bar1 ). Both express, in equivalent terms, the work in foot-pounds (newton-meters) the pump is capable of doing on each unit weight (force) of liq- uid pumped at the rated flow.2 It is the responsibility of the purchaser to determine the required pump total head so the supplier can make a proper pump selection. Underesti- mating the total head required will result in a centrifugal pump’s delivering less than the desired flow through the system.An underestimate of the differential pressure required will result in a positive displacement pump’s using more power than estimated, and the design pressure limit of the pump could be exceeded. Therefore, system pressure and resistance to flow, which are dependent on system characteristics, dictate the required pump head rating. THE PUMPING SYSTEM _______________________________________________ The piping and equipment through which the liquid flows to and from the pump constitute the pumping system. Only the length of the piping containing liquid controlled by the 3. 3. 8.4 CHAPTER EIGHT FIGURE 1 Length of system controlled by pump FIGURE 2 Branch-line pumping system FIGURE 3 Pumps in series and in parallel action of the pump is considered part of the system. A pump and the limit of its system length are shown in Figure 1. The pump suction and discharge piping can consist of branch lines, as shown in Fig- ure 2. There can be more than one pump in a pumping system. Several pumps can be piped together in series or in parallel or both, as shown in Figure 3. When there is more than one pump, the flow through the system is determined by the combined perfor- mance of all the pumps. The system through which the liquid is pumped offers resistance to flow for several reasons. Flow through pipes is impeded by friction. If the liquid discharges to a higher ele- vation or a higher pressure, additional resistance is encountered. The pump must there- fore overcome the total system resistance due to friction and, as required, produce an increase in elevation or pressure at the desired rate of flow. System requirements may be such that the pump discharges to a lower elevation or pressure but additional pump head is still required to overcome pipe friction and obtain the desired rate of flow. ENERGY IN AN INCOMPRESSIBLE LIQUID _______________________________ The work done by a pump is the difference between the energy level at the point where the liquid leaves the pump and the energy level at the point where the liquid enters the pump. Work is also the amount of energy added to the liquid in the system. The total energy at any point in a pumping system is a relative term and is measured relative to some arbi- trarily selected datum plane. 4. 4. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.5 An incompressible liquid can have energy in the form of velocity, pressure, or elevation. Energy in various forms is added to the liquid as it passes through the pump, and the total energy added is constantly increasing with flow. It is appropriate then to speak of the energy added by a pump as the energy added per unit of weight (force) of the liquid pumped, and the units of energy expressed this way are foot-pounds per pound (newton- meters per newton) or just feet (meters). Therefore, when adding together the energies in their various forms at some point, it is necessary to express each quantity in common equivalent units of feet (meters) of head. Liquid flowing in a conduit can undergo changes in energy form. Bernoulli’s theorem for an incompressible liquid states that in steady flow, without losses, the energy at any point in the conduit is the sum of the velocity head, pressure head, and elevation head and that this sum is constant along a streamline in the conduit. Therefore, the energy at any point in the system relative to a selected datum plane is (1) where H energy (total head) of system, ft lb/lb or ft (N m/N or m) V velocity, ft/s (m/s) g acceleration of gravity, 32.17 ft/s2 (9.807 m/s2 ) p pressure, lb/ft2 (N/m2 ) g specific weight (force) of liquid, lb/ft3 (N/m3 ) Z elevation above () or below (—) datum plane, ft (m) The velocity and pressure at the point of energy measurement are expressed in units of equivalent head and are added to the distance Z that this point is above or below the selected datum plane. If pressure is measured as gage (relative to atmosphere), total head H is gage; if pressure is measured as absolute, total head H is absolute. Equation 1 can also be applied to liquid at rest in a vertical column or in a large vessel (or to liquids of var- ious densities) to account for changes in pressure with changes in elevation or vice versa. The equivalent of velocity and pressure energy heads in feet (meters) can be thought of as the height to which a vessel of liquid of constant density has to be filled, above the point of measurement, to create this same velocity or pressure. This is illustrated in Fig- ure 4 and further explained in the following text. Velocity Head The kinetic energy in a mass of flowing liquid is mV2 or (W/g)V2 . The kinetic energy per unit weight (force) of this liquid is (WV2 /Wg), or V2 /2g, measured in feet (meters). This quantity is theoretically equal to the equivalent static head of liquid that is required in a vessel above an opening if the discharge is to have a velocity equal to V. This is also the theoretical height the jet of liquid would rise if it were discharging vertically upward from an orifice. A free-falling particle in a vacuum acquires the velocity V starting from rest after falling a distance H. Also All liquid particles moving with the same velocity have the same velocity head, regard- less of specific weight. The velocity of liquid in pipes and open channels invariably varies across any one section of the conduit. However, when calculating system resistance it is sufficiently accurate to use the average velocity, computed by dividing the flow rate by the cross-sectional area of the conduit, when substituting in the term V2 /2g. Pressure Head The pressure head, or flow work, in a liquid is p/g, with units in feet (meters). A liquid, having pressure, is capable of doing work, for example, on a piston hav- ing an area A and stroke L. The quantity of liquid required to complete one stroke is gAL. The work (force stroke) per unit weight (force) is pAL/gAL, or p/g. The work a pump V 22gH 1 2 1 2 1 2 H V2 2g p g Z 5. 5. 8.6 CHAPTER EIGHT FIGURE 4 Equivalent static head FIGURE 5 Liquids of different specific weights (also specific gravities) require different column heights or pressure heads to produce the same pressure intensity (43.3 lb/in2 298.5 kPa). must do to produce pressure intensity in liquids having different specific weights varies inversely with the specific weight or specific gravity of the liquid. Figure 5 illustrates this point for liquids having specific gravities of 1.0 and 0.5. The less dense liquid must be raised to a higher column height to produce the same pressure as the denser liquid. The pressure at the bottom of each liquid column H is the weight of the liquid above the point of pressure measurement divided by the cross-sectional area A at the same point, AHg/A, which is simply Hg. Note that in this discussion A is in square feet (square meters) and L and H are in feet (meters). The height of the liquid column in feet (meters) above the point of pressure measure- ment, if the column is of constant density, is equivalent pressure static head. When pres- sure intensity AHg/A is substituted for p in p/g, it can be seen that the pressure head H is the liquid column height. Therefore, at the base of equal columns containing different liq- uids (with equal surface pressures), the pressure heads in feet (meters) are the same but the intensities in pounds per square foot (newtons per square meter) are different. For this reason, it is necessary to identify the liquids when comparing pressure heads. Elevation Head The elevation energy, or potential energy, in a liquid is the distance Z in feet (meters) measured vertically above or below an arbitrarily selected horizontal datum plane. Liquid above a reference datum plane has positive potential energy because it can fall a distance Z and acquire kinetic energy or vertical head equal to Z. Also, it requires WZ ft lb (N m) of work to raise W lb (N) of liquid above the datum plane. The work per unit weight (force) of liquid is therefore WZ/W, or Z ft (m). In a pumping system, the energy required to raise a liquid above a reference datum plane can be thought of as being provided by a pump located at the datum elevation and producing a pressure that will support the total weight of the liquid in a pipe between the pump discharge and the point in the pipe to which the liquid is to be raised. This pressure is AZg/A, or simply Zg lb/ft2 (N/m2 ) or Zy/144 lb/in2 . Because head is equal to pressure divided by specific weight, elevation head is Zg/g, or Z ft. Liquid below the reference datum plane has negative elevation head. Total Head Figure 6 illustrates a liquid under pressure in a pipe. To determine the total head at the pressure gage connection and relative to the datum plane, Eq. 1 may be used (assume that the gage is at the pipe centerline): H V2 2g p g Z 6. 6. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.7 FIGURE 6 The total head, or energy, in foot-pounds per pound (newtonmeters per newton) is equal to the sum of the velocity, pressure, and elevation heads relative to a datum place. A unit weight (force) of the same liquid or any liquid raised to rest at the height shown, or under a column of liquid of this same height, has the same head as the unit weight (force) of liquid shown flowing in the pipe. In USCS units In SI units The total head may also be calculated using the expression In USCS units In SI units The total head of 41.84 ft (12.75 m) is equivalent to 1 lb (N) of the liquid raised 41.48 ft (12.75 m) above the datum plane (zero velocity) or the pressure head of 1 lb (N) of the liq- uid under a column height of 41.84 ft (12.75 m) measured at the datum plane. The gage pressure p, and consequently the pressure head, are measured relative to atmospheric pressure. Gage pressure head can therefore be a positive or a negative quan- tity.The pressure may also be expressed as an absolute pressure (measured from complete vacuum). Therefore, when velocity, pressure, and elevation heads are combined to obtain the total energy at a point, it should be clearly stated that the total head is either feet (meters) gage or feet (meters) absolute with respect to the datum plane. The pressure or velocity of a liquid may at times be given as a pressure head of a liq- uid having a density different from the density of the liquid being pumped. In the total head, that is, the sum of the pressure, velocity, and elevation heads, the components must be corrected to be equal to the head of the liquid being pumped. For example, if the pres- sure is measured by a manometer to be 24 in (61 cm) of mercury (sp. gr. 13.6) absolute, 12.75 N # m>N, or m H 0.683 10.55 1.52 41.84 ft # lb>lb, or ft H 2.24 34.6 5 H V2 2g manometer height Z 12.75 Nиm>N, or m 0.683 10.55 1.52 H 3.662 2 9.807 103.4 1000 9802 1.52 41.84 ftиlb>lb, or ft 2.24 34.6 5 H 122 2 32.17 144 15 62.4 5 7. 7. 8.8 CHAPTER EIGHT FIGURE 7 Centrifugal pump total head the pressure head, or energy, in foot-pounds per pound (newton-meters per newton) of water pumped at 60°F (15.6°C) is found as follows. Let subscripts 1 and 2 denote different liquids or, in this example, mercury and water, respectively: (2) (3) Therefore in USCS units in SI units Also, h2 (27.2— 13.6)( ) 6.8 ft [(8.3 13.6)( ) 2.04 m] gage if corrected to a standard barometer of 30 in (76 cm) of mercury. PUMP TOTAL HEAD___________________________________________________ The total head of a pump is the difference between the energy level at the pump discharge (point 2) and that at the pump suction (point 1), as shown in Figures 7 and 8. Applying Bernoulli’s equation (Eq. 1) at each point, the pump total head TH in feet (meters) becomes (4) The equation for pump differential pressure P in pounds per square foot (newtons per square meter) is (5) P¢ in lb>in2 P¢ in lb>ft2 144 P¢ Pd Ps cpd gd aZd V2 d 2g b d cps gs aZs V2 s 2g b d TH Hd Hs a V2 d 2g pd gd Zdb a V2 s 2g ps gs Zsb 76 100 30 12 h2 13.6 1 61 100 8.3 m abs h2 13.6 1 24 12 27.2 ft abs sp. gr.1 sp. gr.2 h1 g1 g1 h1 h2 p2 g2 h1g2 g2 p1 h1g1 p2 h1 p1 g1 8. 8. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.9 FIGURE 8 Example 1 where the subscripts d and s denote discharge and suction, respectively, and H total head of system, () or (—) ft (m) gage or () ft (m) abs P total pressure of system, () or (—) lb/ft2 (N/m2 ) gage or () lb/ft2 (N/m2 ) abs V velocity, ft/s (m/s) p pressure, () or (—) lb/ft2 (N/m2 ) gage or () lb/ft2 (N/m2 ) abs Z elevation above () or below (—) datum plane, ft (m) g specific weight (force) of liquid, lb/ft3 (N/m3 ) g acceleration of gravity, 32.17 ft/s2 (9.807 m/s2 ) Pump total head TH and pump differential pressure P are always absolute quantities because either gage pressures or absolute pressures but not both are used at the discharge and suction connections of the pump and a common datum plane is selected. Pump total head in feet (meters) and pump differential pressure in pounds per square foot (newtons per square meter) are related to each other as (6) It is very important to note that, if the rated total head of a centrifugal pump is given in feet (meters), this head can be imparted to all individual liquids pumped at the rated capacity and speed, regardless of the specific weight (force) of the liquids as long as their viscosities are approximately the same. A pump handling different liquids of approxi- mately the same viscosity will generate the same total head but will not produce the same differential pressure, nor will the power required to drive the pump be the same. On the other hand, a centrifugal pump rated in pressure units would have to have a different pressure rating for each liquid of different specific weight (force). In this section, pump total head will be expressed in feet (meters), the usual way of rating centrifugal pumps. For an explanation of positive displacement pump differential pressure, its use and rela- tionship to pump total head, see Chapter 3. Pump total head can be measured by installing gages at the pump suction and dis- charge connections and then substituting these gage readings into Eq. 4. Pump total head may also be found by measuring the energy difference between any two points in the pumping system, one on each side of the pump, providing all losses (other than pump losses) between these points are credited to the pump and added to the energy head dif- ference. Therefore, between any two points in a pumping system where the energy is added only by the pump and the specific weight (force) of the liquid does not change (for example, as a result of temperature), the following general equation for determining pump total head applies: (7) a V2 2 2g p2 g Z2b a V2 1 2g p1 g Z1b hf 11 22 TH 1H2 H12 hf 11 22 TH P¢ g 9. 9. 8.10 CHAPTER EIGHT where the subscripts 1 and 2 denote points in the pumping system anyplace upstream and downstream from the pump, respectively, and H total head of system, () or (—) ft (m) gage or () ft (m) abs V velocity, ft/s (m/s) p pressure, () or (—) lb/in2 (N/m2 ) gage or () lb/in2 (N/m2 ) abs Z elevation above () or below (—) datum plane, ft (m) g specific weight (force) of liquid (assumed the same between points), lb/ft3 (N/m3 ) g acceleration of gravity, 32.17 ft/s2 (9.807 m/s2 ) hf sum of piping losses between points, ft (m) When the specific gravity of the liquid is known, the pressure head may be calculated from the following relationships: In feet (8a) In meters (8b) The velocity in a pipe may be calculated as follows: In feet per second (9a) In meters per second (9b) The following example illustrates the use of Eqs.4 and 7 for determining pump total head. EXAMPLE 1 A centrifugal pump delivers 1000 gpm (227 m3 /hr) of liquid of specific gravity 0.8 from the suction tank to the discharge tank through the piping shown in Figure 8. (a) Calculate pump total head using gages and the datum plane selected. (b) Calculate total head using the pressures at points 1 and 2 and the same datum plane as (a). Given: Suction pipe ID 8 in (203 mm), discharge pipe ID 6 in (152 mm), hf pipe, valve, and fitting losses, hfs 3 ft (0.91 mm), hfd 25 ft (7.62 m). In USCS units In SI units Calculated pipe velocity 1m3 >h213.542 1ID in cm22 Vd 1000 0.408 62 11.33 ft>s Vs 1000 0.408 82 6.38 ft>s Calculated pipe velocity 1gpm210.4082 1ID in inches22 V 1m3 >h213.542 1pipe ID in cm22 or 1liters>s2112.72 1pipe ID in cm22 V 1gm210.4082 1pipe ID in inches22 p g 0.102 kPa sp. gr. or 1.02 103 bar sp. gr. p g 0.016 lb>ft2 sp. gr. or 2.3 lb>in2 sp. gr. 10. 10. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.11 (a) From Eq. 4, and Eq. 8, in USCS units in SI units Therefore, in USCS units In SI units (b) from Eq. 7, and Eq. 8, in USCS units in SI units Therefore in USCS units 399 152 28 372 ft # lb>lb, or ft TH a0 2.31 100 0.8 50b 10 0 52 13 252 p g 0.102 kPa sp. gr. p g 2.31 lb>in2 sp. gr. TH a V2 2 2g p2 g Z2b a V2 1 2g p1 g Z1b hf 11 22 110.9 1 2.432 113.3 N # m>N, or m TH a 3.482 2 9.807 0.102 855 0.8 1.22b a 1952 2 9.807 0.102125.42 0.8 2b 364 182 372 ft # lb>lb, or ft TH a 11.332 2 32.3 2.31 124 0.8 4b a 6382 2 32.2 2.3113.682 0.8 2b p g 0.102 kPa sp. gr. p g 2.31 lb>in2 sp. gr. TH a V2 d 2g pd gd Zdb a V2 s 2g ps gs Zsb Vd 227 3.54 15.22 3.48 m>s Vs 227 3.54 20.32 1.95 m>s 11. 11. 8.12 CHAPTER EIGHT FIGURE 9 Energy and hydraulic gradients in SI units ENERGY AND HYDRAULIC GRADIENT __________________________________ The total energy at any point in a pumping system may be calculated for a particular rate of flow using Bernoulli’s equation (Eq. 1). If some convenient datum plane is selected and the total energy, or head, at various locations along the system is plotted to scale, the line drawn through these points is called the energy gradient. Figure 9 shows the variation in total energy H measured in feet (meters) from the suction liquid surface point 3 to the dis- charge liquid surface point 4. A horizontal energy gradient indicates no loss of head. The line drawn through the sum of the pressure and elevation heads at various points represents the pressure variation in flow measured above the datum plane. It also repre- sents the height the liquid would rise in vertical columns relative to the datum plane when the columns are placed at various locations along pipes having positive pressure anywhere in the system.This line, shown dotted in Figure 9, is called the hydraulic gradient. The dif- ference between the energy gradient line and the hydraulic gradient line is the velocity head in the pipe at that point. The pump total head is the algebraic difference between the total energy at the pump discharge (point 2) and the total energy at the pump suction (point 1). SYSTEM-HEAD CURVES ______________________________________________ A pumping system may consist of piping, valves, fittings, open channels, vessels, nozzles, weirs, meters, process equipment, and other liquid-handling conduits through which flow is required for various reasons. When a particular system is being analyzed for the pur- 103.2 11.522 8.53 113.3 N # m>N, or m TH a0 0.102 689.5 0.8 15.24b 10 0 1.522 10.91 7.622 12. 12. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.13 FIGURE 10 Construction of system total-head curve pose of selecting a pump or pumps, the resistance to flow of the liquid through these var- ious components must be calculated. It will be explained in more detail later in this sec- tion that the resistance increases with flow at a rate approximately equal to the square of the flow through the system. In addition to overcoming flow resistance, it may be neces- sary to add head to raise the liquid from suction level to a higher discharge level. In some systems the pressure at the discharge liquid surface may be higher than the pressure at the suction liquid surface, a condition that requires more pumping head. The latter two heads are fixed system heads, as they do not vary with rate of flow. Fixed system heads can also be negative, as would be the case if the discharge level elevation or the pressure above that level were lower than suction elevation or pressure. Fixed system heads are also called static heads. A system-head curve is a plot of total system resistance, variable plus fixed, for various flow rates. It has many uses in centrifugal pump applications. It is preferable to express system head in feet (meters) rather than in pressure units because centrifugal pumps are rated in feet (meters), as previously explained. System-head curves usually show flow in gallons per minute, but when large quantities are involved, the units of cubic feet per sec- ond or million gallons per day are used.Although the standard SI units for volumetric flow are cubic meters per second, the units of cubic meters per hour are more common. When the system head is required for several flows or when the pump flow is to be determined, a system-head curve is constructed using the following procedure. Define the pumping system and its length. Calculate (or measure) the fixed system head, which is the net change in total energy from the beginning to the end of the system due to elevation or pressure head differences.An increase in head in the direction of flow is a positive quantity. Next, calculate, for several flow rates, the variable system total head loss through all pip- ing, valves fittings, and equipment in the system. As an example, see Figure 10, in which the pumping system is defined as starting at point 1 and ending at point 2. The fixed sys- tem head is the net change in total energy.The total head at point 1 is ps/g, and that at point 2 is pd/g Z.The pressure and liquid levels do not vary with flow.The variable system head is pipe friction (including valves and fittings).The fixed head and variable heads for several flow rates are added together, resulting in a curve of total system head versus flow. The flow produced by a centrifugal pump varies with the system head, whereas the flow of a positive displacement pump is independent of the system head. By superimposing the head-capacity characteristic curve of a centrifugal pump on a system-head curve, as shown in Figure 10, the flow of a pump can be determined.The curves will intersect at the flow rate of the pump, as this is the point at which the pump head is equal to the required system 13. 13. 8.14 CHAPTER EIGHT FIGURE 11 System total-head curve for Example 1 head for the same flow. When a pump is being purchased, it should be specified that the pump head-capacity curve intersect the system-head curve at the desired flow rate. This intersection should be at the pump’s best efficiency capacity or very close to it. The system-head curve for Example 1 is shown in Figure 11. This assumes that the suction and discharge liquid levels are 5 ft (1.5 m) below and 50 ft (15 m) above the datum plane, respectively, and do not vary with flow. The pressure in the discharge tank is also independent of flow and is 100 lb/in3 (689.5 kPa) gage.These values are therefore fixed sys- tem heads. The pipe and fitting losses are assumed to vary with flow as a square function. The length of the pumping system is from point 1 to point 2. The difference in heads at these points plus the frictional losses at various flow rates are the total system head and the head required by a pump for the different flows. It is necessary to calculate the total system head for only one flow rate—say, design—which in this example is 1000 gpm (227 m3 /h). The total head at other flow conditions is the fixed system head plus the variable system head multiplied by (gpm/1000)2 (m3 /h 227)2 . If Example 1 is an existing system, the total head may be calculated by using gages at the pump suction and discharge con- nections. The total head measured will then be the head at the intersection of the pump and system curves, as shown in Figure 11. In this example, a correctly purchased pump would produce a total head of 372 ft (113 m) at the design flow of 1000 gpm (227 m3 /h). In systems that are open-ended and in which there is a decrease in elevation from inlet to outlet, a portion of the systemhead curve will be negative (Figure 12). In this example, the pump is used to increase gravity flow.Without a pump in the system, the negative resistance, or static head,is the driving head that moves the liquid through the system.Steady-state grav- ity flow is sustained at the flow rate corresponding to zero total system head (negative static head plus system resistance equals zero). If a flow is required at any rate greater than that which gravity can produce, a pump is required to overcome the additional system resistance. For additional information concerning the construction of system-head curves for flow in branch lines, refer to Section 8.2. VARIANTS IN PUMPING SYSTEMS ______________________________________ For a fixed set of conditions in a pumping system, there is just one total head for each flow rate. Consequently, a centrifugal pump operating at a constant speed can deliver just one flow. In practice, however, conditions in a system vary as a result of either controllable or uncontrollable changes. Changes in the valve opening in the pump discharge or bypass line, changes in the suction or discharge liquid level, changes in the pressures at these lev- els, the aging of pipes, changes in the process, changes in the number of pumps pumping 14. 14. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.15 FIGURE 12 Construction of system total-head curve to determine gravity flow and centrifugal pump flow FIGURE 13 Construction of system total-head curves for a pumping system having variable static head into a common header, changes in the size, length, or number of pipes are all examples of either controllable or uncontrollable system changes. These changes in system conditions alter the shape of the system-head curve and, in turn, affect pump flow. Methods of constructing system-head curves and determining the resultant pump flows for two of the more common of these variants are explained here. Variable Static Head In a system where a pump is taking suction from one reservoir and filling another, the capacity of a centrifugal pump will decrease with an increase in static head. The system-head curve is constructed by plotting the variable system friction head versus flow for the piping. To this is added the anticipated minimum and maximum static heads (difference in discharge and suction levels). The resulting two curves are the total system heads for each condition. The flow rate of the pump is the point of intersec- tion of the pump head-capacity curve with either one of the latter two system-head curves or with any intermediate system-head curve for other level conditions. A typical head ver- sus flow curve for a varying static head system is shown in Figure 13. If it is desired to maintain a constant pump flow for different static head conditions, the pump speed can be varied to adjust for an increase or decrease in the total system head. A typical variable-speed centrifugal pump operating in a varying static head system can have a constant flow, as shown in Figure 14. 15. 15. 8.16 CHAPTER EIGHT FIGURE 14 Varying centrifugal pump speed to maintain constant flow for the different reservoir levels shown in Figure 13 FIGURE 15 Construction of system total-head curves for various valve openings It is important to select a pump that will have its best efficiency within the operat- ing range of the system and preferably at the condition at which the pump will operate most often. Variable System Resistance A valve or valves in the discharge line of a centrifugal pump alter the variable frictional head portion of the total system-head curve and conse- quently the pump flow. Figure 15, for example, illustrates the use of a discharge valve to change the system head for the purpose of varying pump flow during a shop performance test. The maximum flow is obtained with a completely open valve, and the only resistance to flow is the friction in the piping, fittings, and flowmeter. A closed valve results in the pump’s operating at shutoff conditions and produces maximum head. Any flow between maximum and shutoff can be obtained by proper adjustment of the valve opening. DIVIDING TOTAL HEAD AND SYSTEM-HEAD CURVES FOR CENTRIFUGAL PUMPS IN SERIES__________________________________ Pump limitations or system component requirements may determine that two or more pumps must be used in series. There are practical limitations as to the maximum head that can be developed in a single pump, even if multistaged. When pumping through sev- eral system components, there may be pressure limitations that prevent using a single pump to develop all of the head required at the beginning of the system. If several pumps are to be used in series, how should the total head be divided among them? The sum of the total heads of the pumps must be equal to the required total system head at the design flow.Although mathematically any division of the total head among the pumps to be used is possible (at long as the sum of the pump heads is equal to the total system head), the actual pressure required at various locations along the system flow path determines how the pumping heads are to be divided. An energy or pressure gradient should be drawn for the system. The number of pumps, their locations, and their total heads should be selected to produce the desired pressures (or range of pressures) at criti- cal locations along the system. In addition to considering the pressure loss through com- ponents to overcome resistance to flow, consideration should also be given to the minimum pressures required to prevent flashing in piping, cavitation at pump inlets, and so on, as well as the maximum working pressures for different parts of the system. If preferred, the total system can be divided into subsystems, one for each pump (or group of pumps). The end of one subsystem and the beginning of another can be selected anywhere between pumps in series because the pump total head will be unaffected by the division line. Consequently, several system-head curves can be drawn for specification and 16. 16. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.17 purchasing purposes—for example, primary condensate pump system, secondary conden- sate pump system, feed pump system, in a total power plant system. TRANSIENTS IN SYSTEM HEADS _______________________________________ During the starting of a centrifugal pump and prior to the time normal flow is reached, certain transient conditions can produce or require heads and consequently torques much higher than design. In some cases, the selection of the driver and the pump must be based on starting rather than normal flow conditions. Low- and medium-specific-speed pumps of the radial- and mixed-flow types (less than approximately 5000 specific speed, rpm, gpm, ft units) have favorable starting character- istics. The pump head at shutoff is not significantly higher than that at normal flow, and the shutoff torque is less than that at normal flow. High-specific-speed pumps of the mixed- and axial-flow types (greater than approximately 5000 specific speed) develop relatively high shutoff heads, and their shutoff torque is greater than that at normal flow. These characteristics of high-specific-speed pumps require special attention during the starting period. Characteristics of pumps of different specific speeds are shown in Figures 16a and 16b. Starting Against a Closed Valve When any centrifugal pump is started against a closed discharge valve, the pump head will be higher than normal. The shutoff head will vary with pump specific speed. As shown in Figure 16a, the higher the specific speed, the higher the shutoff head in percent of normal pump head. As a pump is accelerated from rest to full speed against a closed valve, the head on the pump at any speed is equal to the square of the ratio of the speed to the full speed times the shutoff head at full speed. Therefore, during starting, the head will vary from point A to point E in Figure 17. Points B, C, and D represent intermediate heads at intermediate speeds.The pump, the discharge valve, and any intermediate piping must be designed for maximum head at point E. Pumps requiring less shutoff power and torque than at normal flow condition are usu- ally started against a closed discharge valve. To prevent backflow from a static discharge head prior to starting, either a discharge shutoff valve, a check valve, or a broken siphon is required. When pumps are operated in parallel and are connected to a common dis- charge header that would permit flow from an operating pump to circulate back through an idle pump, a discharge valve or check valve must be used. Figure 18 is a typical characteristic curve for a low-specific-speed pump. Figure 19 illus- trates the variation of torque with pump speed when the pump is started against a closed discharge valve. The torque under shutoff conditions varies as the square of the ratio of speeds, similar to the variation in shutoff head, and is shown as curve ABC. At zero speed, the pump torque is not zero as a result of static friction in the pump hearings and stuffing box or boxes.This static friction is greater than the sum of running friction and power input to the impeller at very low speeds, which explains the dip in the pump torque curve between 0 and 10% speed. Also shown in Figure 19 is the speed-torque curve of a typical squirrel- cage induction motor. Note that the difference between motor and pump torque is the excess torque available to accelerate the pump from rest to full speed. During acceleration, the pump shaft must transmit not only the pump torque (curve ABC) but also the excess torque available in the motor. Therefore pump shaft torque follows the motor speed-torque curve less the torque required to accelerate the mass inertia (WK2 ) of the motor’s rotor. High-specific-speed pumps, especially propeller pumps, requiring more than normal torque at shutoff are not normally started with a closed discharge valve because larger and more expensive drivers would be required. These pumps will also produce relatively high pressures in the pump and in the system between pump and discharge valve. Figure 20 is a typical characteristic curve for a high-specific-speed pump. Curve ABC of Figure 21 illustrates the variation of torque with speed when this pump is started against a closed discharge valve. A typical speed-torque curve of a squirrel-cage induction motor sized for normal pump torque is also shown. Note that the motor has insufficient torque to accel- erate to full speed and would remain overloaded at point C until the discharge valve on the 17. 17. 8.18 CHAPTER EIGHT FIGURE 16A Approximate comparison of head and efficiency versus flow for impellers of different specific speeds in single-stage volute pumps. Specific speed To convert to other units using rpm, m3 /s, m: multiply by 0.01936; rpm, m3 /h, m: multiply by l.163; rpm, L/s, m: multiply by 0.6123 To convert to the universal specific speed s (defined in Section 2.1) divide ns by 2733. ns rpm 2gpm>TH in ft3>4 FIGURE 16B Approximate comparison of power and torque versus flow for impellers of different specific speeds in single-stage volute pumps pump was opened.To avoid this situation, the discharge valve should be timed to open suf- ficiently to keep the motor from overloading when the pump reaches full speed. To accom- plish this timing, it may be necessary to start opening the valve in advance of energizing the motor. Care should be taken not to start opening the discharge valve too soon because 18. 18. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.19 FIGURE 17 Variation in head when a centrifugal pump is started with a closed valve, an open valve, and a check valve FIGURE 18 Typical constant-speed characteristic curves for a low-specific-speed pump FIGURE 19 Variation of torque during start-up of a loss-specific-speed pump with a closed valve, an open valve, and a check valve. See Figure 18 for pump characteristics. FIGURE 20 Typical constant-speed characteristic curves for a high-specific-speed pump this would cause excessive reverse flow through the pump and require the motor to start under adverse reverse-speed conditions. If the driver is a synchronous motor, additional torque at pull-in speed is required, over and above that needed to overcome system head and accelerate the pump and driver rotors from rest.At the critical pull-in point, sufficient torque must be available to pull the load into synchronism in the prescribed time. A syn- chronous motor is started on low-torque squirrel-cage windings prior to excitation of the field windings at the pull-in speed. The low starting torque, the torque required at pull-in, and possible voltage drop, which will lower the motor torque (varies as the square of the voltage), must all be taken into consideration when selecting a synchronous motor to start a high-specific-speed pump against a closed valve. If a high-specific-speed pump is to be started against a closed discharge valve, high starting torques can also be avoided by the use of a bypass valve (see Section 8.2) or by an adjustable-blade pump.1 19. 19. 8.20 CHAPTER EIGHT FIGURE 21 Variation of torque during start-up of a high-specific-speed pump with a closed valve, an open valve, and a check valve. See Figure 20 for pump characteristics. Starting Against a CheckValve A check valve can be used to prevent reverse flow from static head or head from other pumps in the system. The check valve will open automat- ically when the head from the pump exceeds system head. When a centrifugal pump is started against a check valve, pump head and torque follow shutoff values until a speed is reached at which shutoff head exceeds system head. As the valve opens, the pump head continues to increase, and, at any flow, the head will be that necessary to overcome sys- tem static head or head from other pumps, frictional head, valve head loss, and the iner- tia of the liquid being pumped. Figure 19, curve ABD, illustrates speed-torque variation when a low-specific-speed pump is started against a check valve with static head and system friction as shown in Figure 18. Figure 21, curve ABD, illustrates speed-torque variation for a high-specific- speed pump started against a cheek valve with static head and system friction as shown in Figure 20.The use of a quick-opening check valve with highspecific-speed pumps elim- inates starting against higher than full-open valve shutoff heads and torques. The speed-torque curves shown for the period during the acceleration of the liquid in the system have been drawn with the assumption that the head required to accelerate the liquid and overcome inertia is insignificant. Acceleration head is discussed in more detail later. Starting Against an Open Valve If a centrifugal pump is to take suction from a reser- voir and discharge to another reservoir having the same liquid elevation or the same equiv- alent total pressure, it can be started without a shutoff discharge valve or check valve. The system-head curve is essentially all frictional plus the head required to accelerate the liq- uid in the system during the starting period. Neglecting liquid inertia, the pump head would not be greater than normal at and speed during the starting period, as shown in curve AFGHI of Figure 17. Pump torque would not be greater than normal at any speed during the starting period, as shown in Figures 19 and 21, curves AD. Pump head and torque at any speed are equal to their values at normal condition times the square of the ratio of the speed to full speed, whereas the capacity varies directly with this ratio. Starting a Pump Running in Reverse When a centrifugal pump discharges against a static head or into a common discharge header with other pumps and is then stopped, the flow will reverse through the pump unless the discharge valve is closed or unless there is a check valve in the system or a broken siphon in a siphon system. If the pump does not have a nonreversing device, it will turn in the reverse direction. A pump that discharges against a static head through a siphon system without a valve will have reverse flow and speed when the siphon is being primed prior to starting. Figures 22 and 23 illustrate typical reverse-speed-torque characteristics for a low- and a high-specific-speed pump.When flow reverses through a pump and the driver offers very 20. 20. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.21 FIGURE 22 Typical reverse-speed-torque characteristics of a low-specific-speed, radial-flow, doublesuction pump FIGURE 23 Typical reverse-speed-torque characteristics of a high-specific-speed, axial-flow, diffuser pump little or no torque resistance, the pump will reach higher than normal forward speed in the reverse direction. This runaway speed will increase with specific speed and system head. Shown in Figures 22 and 23 are speed, torque, head, and flow, all expressed as a percent- age of the pump design conditions for the normal forward speed. When a pump is running in reverse as a turbine under no load, the head on the pump will be static head (or head from other pumps) minus head loss as a result of friction due to the reverse flow. If an attempt is made to start the pump while it is running in reverse, an electric motor must apply positive torque to the pump while the motor is initially running in a negative direction. Figures 22 and 23 show, for the two pumps, the torques required to decelerate, momentarily stop, and then accelerate the pump to normal speed. If either of these pumps were pumping into an all-static-head system, starting it in reverse would require over- coming 100% normal head, and it can be seen that a torque in excess of normal would be required by the driver while the driver is running in reverse. In addition to overcoming positive head, the driver must add additional torque to the pump to change the direction of the liquid. This could result in a prolonged starting time under higher than normal cur- rent demand. Characteristics of the motor, pump, and system must be analyzed together 21. 21. 8.22 CHAPTER EIGHT FIGURE 24 Transient system head as a result of liquid acceleration and system friction when a propeller pump is started with an open valve to determine actual operating conditions during this transient period. Starting torques requiring running in reverse become less severe when the system head is partly or all fric- tion head. Inertial Head If the system contains an appreciable amount of liquid, the inertia of the liquid mass could offer a significant resistance to any sudden change in velocity. Upon starting a primed pump and system without a valve, all the liquid in the system must accelerate from rest to a final condition of steady flow. Figure 24 illustrates a typical sys- tem head resistance that could be produced by a propeller pump pumping through a fric- tion system when accelerated from rest to full speed. If the pump were accelerated very slowly, it would produce an all-friction resistance with zero liquid acceleration varying with flow approaching curve OABCDEF. Individual points on this curve represent system resis- tance at various constant pump speeds. If the pump were accelerated very rapidly, it would produce a system resistance approaching curve OGHIJKL. This is a shutoff condition that cannot be realized unless infinite driver torque is available. Individual points on this curve represent a system resistance at various constant speeds with no flow, which is the same as operating with a closed discharge valve. Curve LF represents the maximum total head the pump can produce as a result of both system friction and inertia at 100% speed. Head variation from L to F is a result of flow through the system, increasing at a decreasing rate of acceleration and increasing friction to the normal operating point F, where all the head is frictional.The actual total system-head resistance curve for any flow condition will be, therefore, the sum of the frictional resistance in feet (meters) for that steady-flow rate plus the inertial resistance, also expressed in feet (meters). The inertial resistance at any flow is dependent on the mass of liquid and the instantaneous rate of change of velocity at the flow condition. A typical total system resistance for a motor-driven propeller pump is shown as OMNPQRF in Figure 24. For a particular pump and system, different driver- speed-torque characteristics will result in a family of curves in the area OLF. The added inertial system head produced momentarily when high-specific-speed pumps are started is important when considering the duration of high driver torques and currents, the pressure rise in the system, and the effect on the pump of operation at high heads and low flows. The approximate acceleration head ha required to change the veloc- ity of a mass of liquid at a uniform rate and cross section is (10)ha L¢V g¢t 22. 22. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.23 where L length of constant-cross-section conduit, ft (m) V velocity change, ft/s (m/s) g acceleration of gravity, 32.17 ft/s2 (9.807 m/s2 ) t time interval, s To calculate the time to accelerate a centrifugal pump from rest or from some initial speed to a final speed, and to estimate the pump head variation during this interim, a trial-and-error solution may be used. Divide the speed change into several increments of equal no-flow heads, such as OGHIKL in Figure 24. For the first incremental speed change, point O to point N1, estimate the total system head, point M, between G and A. Next estimate the total system head, point X, at the average speed for this first incre- mental speed change. These points are shown in Figure 24. Calculate the time in seconds for this incremental speed change to take place using the equation in USCS units (11a) where WK2 total pump and motor rotor weight moment of inertia, W weight (force), K radius of gyration, lb ft2 N incremental speed change, rpm TD motor torque at average speed, ft lb Tp pump torque at average speed, ft lb in SI units (11b) where MK2 total pump and motor rotor mass moment of inertia, M weight (mass), K radius of gyration, kg m2 N incremental speed change, rpm TD motor torque at average speed, N m TP pump torque at average speed, N m In SI units, when diameter of gyration D is used rather than radius of gyration K, and MD2 4MK2 , then (11c) Calculate the acceleration head required to change the flow in the system from point O to point M using Eq. 10 and time from Eq. 11. Add acceleration head to frictional head at the assumed average flow, and if this value is correct, it will fall on the average pump head-capacity curve, point X. Adjust points M and X until these assumed flows result in the total acceleration and frictional heads agreeing with flow X at the average speed. Repeat this procedure for other increments of speed change, adding incremental times to get total accelerating time to bring the pump up to its final speed. Plot system head ver- sus average flow for each incremental speed change during this transient period, as shown in Figure 24. Figures 25 and 26 illustrate how driver and pump torques can be determined from their respective speed-torque curves. Figure 25 is a family of curves that represents the torques required to produce flow against different heads without acceleration of the liquid or pump for the various speeds selected. Pump torque for any reduced speed can be calculated from the full-speed curve using the relation that torque varies as the second power and flow varies as the first power of the speed ratio. Point X is the torque at the average speed and the trial average flow during the first incremental speed change, ¢t MD2 ¢N 38.21TD TP2 ¢t MK2 ¢N 9.551TD TP2 ¢t WK2 ¢N 3071TD TP2 23. 23. 8.24 CHAPTER EIGHT FIGURE 25 Transient total pump torque as a result of liquid acceleration and system friction when a propeller pump is started with an open valve. Pump head characteristics are shown in Figure 24. which is adjusted for different assumed conditions. Figure 26 shows a typical squirrel- cage induction motor speed-torque curve, and, for the purpose of illustration, it has been selected to have the same torque rating as the pump requires at full speed (approxi- mately 97% synchronous speed). Point X in this figure is the motor torque at the average speed during the first incremental speed change. In Figure 26, the developed torque curve for the different speeds shown in Figure 25 is redrawn as the total frictional and inertial pump torque Tp. For the conditions used in this example, and as shown in Figure 26, after approximately 88% synchronous speed, very little excess torque (TD Tp) is available for accelerating the pump and motor rotor inertia. However, as long as an induction motor has adequate torque to drive the pump at the normal condition, full speed will be reached providing the time-current demand can be tolerated. A synchronous motor, on the other hand, may not have sufficient torque to pull into step. Liquid acceleration decreases as motor torque decreases, adjusting to the available excess motor torque. The pump speed changes very slowly during the final period. Figure 26 also shows the motor current for the different speeds and torques. A motor having a higher than normal pump torque rating or a motor having high starting torque characteristics will reduce the starting time, but higher heads will be produced during the acceleration period. Note, however, that heads produced cannot exceed shutoff at any speed. The total torque input to the pump shaft is equal to the sum of the torques required to overcome system friction, liquid inertia, and pump rotor iner- tia during acceleration. Torque at the pump shaft will therefore follow the motor speed- torque curve less the torque required to overcome the motor’s rotor inertia. To reduce the starting inertial pump head to an acceptable amount, if desired, other alternative start- ing schemes can be used. A short bypass line from the pump discharge back to the suc- tion can be provided to divert flow from the main system. The bypass valve is closed slowly after the motor reaches full speed. A variable-speed or a two-speed motor will reduce the inertial head by controlling motor torque and speed, thereby increasing the accelerating time. This procedure for developing the actual system head and pump torque, including liq- uid inertia, becomes more complex if the pump must employ a discharge valve. To avoid high pump starting heads and torques, the discharge valve must be partially open on starting and then opened a sufficient amount before full speed is reached. The valve resis- tance must be added to the system friction and inertia curves if an exact solution is required. 24. 24. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.25 FIGURE 26 Propeller pump and motor speed-torque curves, showing effect of accelerating the liquid in the system during the starting period FIGURE 27 Pumping system using a siphon for head recovery Siphon Head Between any two points having the same elevation in a pumping system, no head is lost because of piping elevation changes because the net change in elevation is zero. If the net change in elevation between two points is not zero, additional pump head is required if there is an increase in elevation and less head is required if there is a decrease in elevation. When piping is laid over and under obstacles with no net change in elevation, no pump- ing head is required to sustain flow other than that needed to overcome frictional and minor losses. As the piping rises, the liquid pressure head is transformed to elevation head, and the reverse takes place as the piping falls.A pipe or other closed conduit that rises and falls is called a siphon, and one that falls and rises is called an inverted siphon. The siphon prin- ciple is valid provided the conduit flows full and free of liquid vapor and air so the densities of the liquid columns are alike. It is this requirement that determines the limiting height of a siphon for complete recovery because the liquid can vaporize under certain conditions. Pressure in a siphon is minimum at the summit, or just downstream from it, and Bernoulli’s equation can be used to determine if the liquid pressure is above or below vapor pressure. Referring to Figure 27, observe the following. The absolute pressure head Hs in feet (meters) at the top of the siphon is 25. 25. 8.26 CHAPTER EIGHT FIGURE 28 Transient system total head priming a siphon (12) where HB barometric pressure head of liquid pumped, ft (m) ZS siphon height to top of conduit ( Z1 if no seal well is used), ft (m) hf (s 2) frictional and minor losses from S to 2 (or 3 if no seal well is used), includ- ing exit velocity head loss at 2 (or 3), ft (m) V2 S/2g velocity head at summit, ft (m) The absolute pressure head at the summit can also be calculated using conditions in the up leg by adding the barometric pressure head to the pump head (TH) and deducting the distance from suction level to the top of the conduit (Z4), the frictional loss in the up leg (hf (1 S)), and the velocity head at the summit. If the suction level is higher than the dis- charge level and flow is by gravity, the absolute pressure head at the summit is found as above and TH 0. Whenever Z1 in Figure 27 is so high that it exceeds the maximum siphon capability, a seal well is necessary to increase the pressure at the top of the siphon above vapor pres- sure. Note Z1 ZS represents an unrecoverable head and increases the pumping head. Water has a vapor pressure of 0.77 ft (23.5 cm) at 68°F (20°C) and theoretically a 33.23-ft- high (10.13-cm) siphon is possible with a 34-ft (10.36-m) water barometer. In practice, higher water temperatures and lower barometric pressures limit the height of siphons used in condenser cooling water systems to 26 to 28 ft (8 to 8.5 m). The siphon height can be found by using Eq. 12 and letting HS equal the vapor pressure in feet (meters). In addition to recovering head in systems such as condenser cooling water, thermal dilution, and levees, siphons are also used to prevent reverse flow after pumping is stopped by use of an automatic vacuum breaker located in the summit. Often siphons are used solely to eliminate the need for valves or flap gates. In open-ended pumping systems, siphons can be primed by external means of air removal. Unless the siphon is primed initially upon starting, a pump must fill the sys- tem and provide a minimum flow to induce siphon action. During this filling period and until the siphon is primed, the siphon head curve must include this additional siphon filling head, which must be provided by the pump. Pumps in siphon systems are usually low-head, and they may not be capable of filling the system to the top of the siphon or of filling it with adequate flow. Low-head pumps are high-specific-speed and require more power at reduced flows than during normal pumping. Figure 28 illustrates the performance of a typical propeller pump when priming a siphon system and during nor- mal operation. HS HB ZS hf 1S22 V2 S 2g 26. 26. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.27 TABLE 1 Values for determining pipe-diameter ratio versus (ft3 /s)/d5/2 in circular pipes 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 . . . 0.0006 0.0025 0.0055 0.0098 0.0153 0.0220 0.0298 0.0389 0.0491 0.1 0.0605 0.0731 0.0868 0.1016 0.1176 0.1347 0.1530 0.1724 0.1928 0.2144 0.2 0.2371 0.2609 0.2857 0.3116 0.3386 0.3666 0.3957 0.4259 0.4571 0.4893 0.3 0.523 0.557 0.592 0.628 0.666 0.704 0.743 0.784 0.825 0.867 0.4 0.910 0.955 1.000 1.046 1.093 1.141 1.190 1.240 1.291 1.343 0.5 1.396 1.449 1.504 1.560 1.616 1.674 1.733 1.792 1.853 1.915 0.6 1.977 2.041 2.106 2.172 2.239 2.307 2.376 2.446 2.518 2.591 0.7 2.666 2.741 2.819 2.898 2.978 3.061 3.145 3.231 3.320 3.411 0.8 3.505 3.602 3.702 3.806 3.914 4.023 4.147 4.272 4.406 4.549 0.9 4.70 4.87 5.06 5.27 5.52 5.81 6.18 6.67 7.41 8.83 All tabulated values are in units of (ft3 /s)/d5/2 ; d diameter, ft; Dcrit critical depth, ft. For SI units, multiply (m3 /h)/m5/2 by 5.03 104 to obtain (ft3 /s)/ft5/2 . Examples 2, 3, and 4 illustrate the use of this table. Source: Reference 13. Dcrit d When a pump and driver are to be selected to prime a siphon system, it is necessary to estimate the pump head and the power required to produce the minimum flow needed to start the siphon. The minimum flow required increases with the length and the diameter and decreases with the slope of the down-leg pipe.2 Prior to the removal of all the air in the system, the pump is required to provide head to raise the liquid up to and over the siphon crest. Head above the crest is required to produce a minimum flow similar to flow over a broad-crested weir.This weir head may be an appreciable part of the total pump head if the pump is lowhead and large-capacity. A conservative estimate of the pump head would include a full conduit above the siphon crest. In reality, the down leg must flow partially empty before it can flow full, and it is accurate enough to estimate that the depth of liquid above the siphon crest is at critical depth for the cross section. Table 1 can be used to estimate criti- cal depth in circular pipes, and Figure 29 can be used to calculate the cross-sectional area of the filled pipe to determine the velocity at the siphon crest. Until all the air is removed and all the piping becomes filled, the down leg is not part of the pumping system, and its frictional and minor losses are not to be added to the max- imum system-head curve to fill and prime the siphon shown in Figure 28. The total head TH in feet (meters) to be produced by the pump in Figure 27 until the siphon is primed is (13) where Z3 distance between suction level and centerline liquid at siphon crest, ft (m) hf(1 s) frictional and minor losses from 1 to S, ft (m) V2 C/2g velocity head at crest using actual liquid depth, approx. critical depth, ft (m) Use of Eq. 13 permits plotting the maximum system-head curve to fill and prime the siphon for different flow rates.The pump priming flow is the intersection of the pump total head curve and this system-head curve.The pump selected must have a driver with power as shown in Figure 28 to prime the system during this transient condition. For the pumping system shown in Figure 27, after the system is primed, the pump total head reduces to (14)TH Z hf1122 TH Z3 hf 11S2 V2 C 2g 27. 27. 8.28 CHAPTER EIGHT FIGURE 29 Area versus depth for a circular pipe In SI units: 1 meter 3.28 feet 1 VD (V in m/s, D in m) 129.2 VD" (V in ft/s, D" in inches) R rVD m 1r in kg>m3 , V in m>s, D in m, m in Nиs>m2 2 where Z distance between suction and seal well levels (or discharge pool level if no seal well is used), ft (m) hf(12) frictional and minor losses from 1 to 2 (or 3 if no seal well is used), includ- ing exit velocity head loss at 2 (or 3), ft (m) Use of Eq. 14 permits plotting of the normal system-head curve with a primed siphon, shown in Figure 28, for different flow rates. The normal pump flow is the intersection of the pump total head curve and the normal system-head curve. If the pump cannot provide sufficient flow to prime the siphon, or if the driver does not have adequate power, the system must be primed externally by a vacuum or jet pump. An auxiliary priming pump can also be used to continuously vent the system because it is necessary that this be done to maintain full siphon recovery. In some systems, the water pumped is saturated with air, and as the liquid flows through the system, the pressure is reduced (and in cooling systems the temperature is increased). Both these conditions cause the release of some of the entrained air. Air will accumulate at the top of the siphon and in the upper parts of the down leg.The siphon works on the principle that an increase in elevation in the up leg produces a decrease in pressure and an equal decrease in ele- vation in the down leg resulting in recovery of this pressure. This cannot occur if the den- sity of the liquid in the down leg is decreased as a result of the formation of air pockets. These air pockets also restrict the flow area. A release of entrained air and air leakage into the system through pipe joints and fittings will result in a centrifugal pump’s deliv- ering less than design flow, as the head will be higher than estimated. Also, high-specific- speed pumps with rising power curves toward shutoff can become overloaded. In order to maintain full head recovery, it is necessary to continuously vent the siphon at the top and at several points along the down leg, especially at the beginning of a change in slope.3 These venting points can be manifolded together and connected to a single downward venting system. Some piping systems may contain several up and down legs; that is, several siphons in series. Each down leg, as in a single siphon, is vulnerable to air or vapor binding. The like- lihood of flow reduction, and conceivably in some cases complete flow shutoff, is increased in a multiple siphon system.3 As shown in Figure 30, system static head is increased if 28. 28. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.29 FIGURE 30 Multiple siphon system (Z normal system static head when pipe is flowing full). Pump flow is stopped when normal static head plus sum of air pocket heights equals pump shutoff head. proper venting is not provided at the top of each siphon. Normally the static head is the dif- ference between outlet and inlet elevations. If air pockets exist, head cannot be recovered and the normal static head is increased by the sum of the heights of all the intermediate liquidless pockets. Flow will stop when the total static head equals the pump shutoff head. The following examples illustrate the use of Eqs.3,9,12,13,and 14,Table 1,and Figure 29. EXAMPLE 2 A pump is required to produce a flow of 70,000 gpm (15,900 m3 /h) through the system shown in Figure 27. Calculate the system total head from point 1 to point 3 (no seal well) under the following conditions: Specific gravity 0.998 for 80°F (26.7°C) water Barometric pressure 29 in (73.7 cm) mercury abs (sp. gr. 13.6) Suction and discharge water levels are equal, Z 0 Z1 40 ft (12.2 m) Hf(1s) 3 ft (0.91 m) up-leg frictional head hf (S3) 3.3 ft (1 m) down-leg frictional head, including exit loss Pipe diameter 48 in (121.9 cm) ID Water vapor pressure 0.507 lb/in2 (3.5 kPa) abs at 80°F (26.7°C) The maximum siphon height may be found from Eq. 12: From Eq. 3 HB barometric pressure head in feet (meters) of liquid pumped In USCS units In SI units HS p g 3.5 1000 9769 0.358 m abs sp. gr.1 sp. gr.2 h1 13.6 0.998 73.7 100 10 m abs HS p g 144 0.507 62.19 1.17 ft abs sp. gr.1 sp. gr.2 h1 13.6 0.998 29 12 32.9 ft abs ZS HB hf 1S32 HS V2 S 2g 29. 29. 8.30 CHAPTER EIGHT From Eqs. 9 and 12, in USCS units in SI units Because the maximum height is exceeded (Z1 Zs), siphon recovery is not possible. The system total head is therefore found from Eq. 13: The critical depth Dcrit is found using Table 1: In USCS units In SI units Convert to USCS units (see footnote to Table 1): To calculate the water velocity at the siphon crest, determine the area of the filled pipe. From Figure 29, ratio of filled area to area of a full pipe is 0.95 for a depth-to-diameter ratio of 0.901: In USCS units From Eq. 13 In SI units Vc m3 >h 0.951ID in cm22 3.54 15,900 0.95 121.92 3.54 3.99 m>s TH 37.8 3 13.02 2 32.17 43.43 ft Z3 40 4 3.6 2 37.8 ft Vc gpm 0.951ID in inches22 0.408 70,000 0.95 482 0.408 13.0 ft>s Dcrit 0.901 1.219 1.1 m Dcrit d 0.901 ft3 >s ft5>2 9695 5.03 104 4.88 m3 >h d5>2 15,900 1.2195>2 9695 Dcrit 0.901 4 3.6 ft Dcrit d 0.901 ft3 >s d5>2 156 45>2 4.88 ft3 >s 70,000 7.481 60 156 TH Z3 hf 11S2 V2 c 2g ZS 10 1 0.358 3.792 2 9.807 9.1 m VS m3 >h 1pipe ID in cm22 3.54 15,900 121.92 3.54 3.79 m>s ZS 32.9 3.3 1.17 12.42 2 32.17 32.63 ft VS gpm 1pipe ID in inches22 0.408 70,000 482 0.408 12.4 ft>s 30. 30. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.31 From Eq. 13 EXAMPLE 3 Calculate the minimum total system head using conditions in Example 2 and a seal well, as shown in Figure 27. Use 2.8 ft (0.853 m) for the frictional head loss hf(s2). The maximum siphon height Zs in Example 2 was found to be 32.63 ft (9.95 m). Therefore from Eq. 14 the total system head after priming is In USCS units In SI units Note that the seal well elevation is above discharge level. Therefore in USCS units in SI units EXAMPLE 4 The dimensions of the down leg in Example 3 require a minimum velocity of 5 ft/s (1.52 m/s) flowing full to purge air from the system and start the siphon. Cal- culate the system head the pump must overcome to prime the siphon. In USCS units In SI units The critical depth is found from Table 1: In USCS units In SI units Convert to USCS units (see footnote to Table 1): Dcrit 0.6 1.219 0.73 m Dcrit d 0.6 ft3 >s d5>2 3902 5.03 104 1.97 m3 >h d5>2 6400 1.2195>2 3902 Dcrit 0.6 4 2.4 ft Dcrit d 0.6 ft3 >s d5>2 62.8 45>2 1.97 m3 >h V1pipe ID in cm22 3.54 1.52 121.92 3.54 6400 ft3 >s 28,200 449 62.8 gpm V1pipe ID in inches22 0.408 5 482 0.408 28,200 TH 2.25 1.763 4.01 m TH 7.37 5.8 13.17 ft Z Z1 ZS 12.2 9.95 2.25 m hf1122 hf11S2 hf1S22 0.91 0.853 1.763 ft Z Z1 ZS 40 32.63 7.37 ft hf1122 hf11S2 hf1S22 3 2.8 5.8 ft TH Z hf1122 TH 11.53 0.91 3.992 2 9.807 13.25 m Z3 12.2 1.219 1.1 2 11.53 m 31. 31. 8.32 CHAPTER EIGHT From Figure 29, the ratio of the filled area to the area of a full pipe is 0.625 for a depth- to-diameter ratio of 0.60: In USCS units In SI units From Eq. 13 In USCS units In SI units If the system is not externally primed, the centrifugal pump selected must be able to deliver at least 28,000 gpm (6400 m3 /h) at 38.68 ft (11.79 m) total head and must be provided with a driver having adequate power for this condition. After the system is primed, the pump must be capable of delivering at least 70,000 gpm (15,900 m3 /h) at 13.17 ft (4.01 m) (see Figure 28). HEAD LOSSES IN SYSTEM COMPONENTS_______________________________ Pressure Pipes Resistance to flow through a pipe is caused by viscous shear stresses in the liquid and by turbulence at the pipe walls. Laminar flow occurs in a pipe when the average velocity is relatively low and the energy head is lost mainly as a result of viscos- ity. In laminar flow, liquid particles have no motion next to the pipe walls and flow occurs as a result of the movement of particles in parallel lines with velocity increasing toward the center. The movement of concentric cylinders past each other causes viscous shear stresses, more commonly called friction. As flow increases, the flow pattern changes, the average velocity becomes more uniform, and there is less viscous shear. As the laminar film decreases in thickness at the pipe walls and as the flow increases, the pipe rough- ness becomes important because it causes turbulence. Turbulent flow occurs when aver- age pipe velocity is relatively high and energy head is lost predominantly because of turbulence caused by the wall roughness. The average velocity at which the flow changes from laminar to turbulent is not definite, and there is a critical zone in which either lam- inar or turbulent flow can occur. Viscosity can be visualized as follows. If the space between two planar surfaces is filled with a liquid, a force will be required to move one surface at a constant velocity relative to the other.The velocity of the liquid will vary linearly between the surfaces.The ratio of the force per unit area, called shear stress, to the velocity per unit distance between surfaces, called shear or deformation rate, is a measure of a liquid’s dynamic or absolute viscosity. TH 12.25 9.12 0.15 2.42 2 9.807 11.79 m hf11S2 at 6400 m3 >h a 6400 15,900 b 2 0.91 0.15 m Z 2.25 m 1from Example 32 Z2 ZS 1.219 Dcrit 2 9.95 1.219 0.73 2 9.1 m TH 17.37 29.832 0.49 82 2 32.17 38.68 ft hf 11S2 at 28,200 gpm a 28,200 70,000 b 2 3 0.49 ft Z 7.37 ft 1from Example 32 Z2 ZS 4 Dcrit 2 32.63 4 2.4 2 29.83 ft TH Z3 hf11S2 Vc 2 2g Vc 1.52 0.625 2.4 m>s Vc 5 0.625 8.0 ft>s 32. 32. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.33 Liquids such as water and mineral oil, which exhibit shear stresses proportional to shear rates, have a constant viscosity for a particular temperature and pressure and are called Newtonian or true liquids. In the normal pumping range, however, the viscosity of true liquids may be considered independent of pressure. For these liquids, the viscosity remains constant because the rate of deformation is directly proportional to the shearing stress.The viscosity and resistance to flow, however, increase with decreasing temperature. Liquids such as molasses, grease, starch, paint, asphalt, and tar behave differently from Newtonian liquids. The viscosity of the former does not remain constant and their shear, or deformation, rate increases more than the stress increases. These liquids, called thixotropic, exhibit lower viscosity as they are agitated at a constant temperature. Still other liquids, such as mineral slurries, show an increase in viscosity as the shear rate is increased and are called dilatant. In USCS units, dynamic (absolute) viscosity is measured in pound-seconds per square foot or slugs per foot-second. In SI measure, the units are newton-seconds per square meter or pascalseconds. Usually dynamic viscosity is measured in poises (1 P 0.1 Pa s) or in centipoises (1 cP P): The viscous property of a liquid is also sometimes expressed as kinematic viscosity. This is the dynamic viscosity divided by the mass density (specific weight/g). In USCS units, kinematic viscosity is measured in square feet per second. In SI measure, the units are square meters per second. Usually kinematic viscosity is measured in stokes (1 St 0.0001 m2 /s) or in centistokes (1 cSt St): A common unit of kinematic viscosity in the United States is Saybolt seconds univer- sal (SSU) for liquids of medium viscosity and Saybolt seconds Furol (SSF) for liquids of high viscosity.Viscosities measured in these units are determined by using an instrument that measures the length of time needed to discharge a standard volume of the sample. Water at 60°F (15.6°C) has a kinematic viscosity of approximately 31 SSU (1.0 cSt). For values of 70 cSt and above, The dimensionless Reynolds number Re is used to describe the type of flow in a pipe flowing full and can be expressed as follows: (15) where V average pipe velocity, ft/s (m/s) D inside pipe diameter, ft (m) y liquid kinematic viscosity, ft2 /s (m2 /s) r liquid density, slugs/ft3 (kg/m3 ) m liquid dynamic (or absolute) viscosity slug/ft s (N s/m2 ) Note: The dimensionless Reynolds number is the same in both USCS and SI units. When the Reynolds number is 2000 or less, the flow is generally laminar, and when it is greater than 4000, the flow is generally turbulent. The Reynolds number for the flow of water in pipes is usually well above 4000, and therefore the flow is almost always turbulent. The Darcy-Weisbach formula is the one most often used to calculate pipe friction. This formula recognizes that friction increases with pipe wall roughness, with wetted surface area, with velocity to a power, and with viscosity and decreases with pipe diameter to a power and with density. Specifically, the frictional head loss hf in feet (meters) is Re VD v rVD m SSU 10 SSF cSt 0.216 SSU 1 ft2 >s 0.0929034 m2 >s 92,903.4 cSt 1 100 1 lb # s>ft2 47.8801 Pa # s 47,880.1 cP 1 100 33. 33. 8.34 CHAPTER EIGHT (16) where f friction factor L pipe length, ft (m) D inside pipe diameter, ft (m) V average pipe velocity, ft/s (m/s) g acceleration of gravity, 32.17 ft/s2 (9.807 m/s2 ) For laminar flow, the friction factor f is equal to 64/Re and is independent of pipe wall roughness. For turbulent flow, f for all incompressible fluids can be determined from the well-known Moody diagram, shown in Figure 31. To determine f, it is required that the Reynolds number and the relative pipe roughness be known. Values of relative roughness /D), where is a measure of pipe wall roughness height in feet (meters), can be obtained from Figure 32 for different pipe diameters and materials. Figure 32 also gives values for f for the flow of 60°F (15.6°C) water in rough pipes with complete turbulence. Values of kinematic viscosity and Reynolds numbers for a number of different liquids at various temperatures are given in Figure 33. The Reynolds numbers of 60°F (15.6°C) water for various velocities and pipe diameters may be found by using the VD" scale in Figure 31. There are many empirical formulas for calculating pipe friction for water flowing under turbulent conditions. The most widely used is the Hazen-Williams formula: In USCS units (17a) In SI units (17b) where V average pipe velocity, ft/s (m/s) C friction factor for this formula, which depends on roughness only r hydraulic radius (liquid area divided by wetted perimeter) or D/4 for a full pipe, ft (m) S hydraulic gradient or frictional head loss per unit length of pipe, ft/ft (m/m) The effect of age on a pipe should be taken into consideration when estimating the fric- tional loss. A lower C value should be used, depending on the expected life of the system. Table 2 gives recommended friction factors for new and old pipes. A value of C of 150 may be used for plastic pipe. Figure 34 is a nomogram that can be used in conjunction with Table 2 for a solution to the Hazen-Williams formula. The frictional head loss in pressure pipes can be found by using either the Darcy- Weisbach formula (Eq. 16) or the Hazen-Williams formula (Eq. 17). Tables in the appendix give Darcy-Weisbach friction values for Schedule 40 new steel pipe carrying water. Tables are also provided for losses in old cast iron piping based on the Hazen-Williams formula with C 100. In addition, values of C for various pipe materials, conditions, and years of service can also be found in the appendix. The following examples illustrate how Figures 31, 32, and 33 and Table 2 may be used. EXAMPLE 5 Calculate the Reynolds number for 175°F (79.4°C) kerosene flowing through 4-in (10.16-cm), Schedule 40, 3.426-in (8.70-cm) ID, seamless steel pipe at a velocity of 14.6 ft/s (4.45 m/s). In USCS units In SI units VD 4.45 0.087 0.387 m>s m 0.387 129.2 50 ft>s in VD– 14.6 3.426 50 ft>s in V 0.8492Cr0.63 S0.54 V 1.318Cr0.63 S0.54 hf f L D V2 2g 34. 34. 8.35 [[A5655]] FIGURE 31 Moody diagram. (Reference 14) In SI units: ( in kg /m3 , V in m/s, D in m, µ in N • s/m2 .) 1 meter 3.28 ft; 1VD (V in m/s, D in m) 129.2 VD– (V in ft/s, D– in inches). R rVD m Reynolds number consistent unitsR VD n 35. 35. 8.36 CHAPTER EIGHT TABLE 2 Values of friction factor C to be used with the Hazen-Williams formula in Figure 34 Type of pipe Age Size, ina C Cast iron New All sizes 130 5 years old 12 and over 120 8 119 4 118 10 years old 24 and over 113 12 111 4 107 20 years old 24 and over 100 12 96 4 89 30 years old 30 and over 16 87 4 75 40 years old 30 and over 83 16 80 4 64 40 and over 77 24 74 4 55 Welded steel Any age, any size Same as for cast iron pipe 5 years old Riveted steel Any age, any size Same as cast iron pipe 10 years older Wood-stave Average value, regardless of age and size 120 Concrete or Large sizes, good workmanship, steel forms 140 concrete- Large sizes, good workmanship, wooden forms 120 lined Centrifugally spun 135 Vitrified In good condition 110 a In 25.4 mm Source: Adapted From Reference 15. Follow the tracer lines in Figure 33 and read directly: EXAMPLE 6 Calculate the frictional head loss for 100 ft (30.48 m) of 20-in (50.8-cm), Schedule 20, 19.350-in (49.15-cm) ID, seamless steel pipe for 109°F (42.8°C) water flow- ing at a rate of 11,500 gpm (2612 m3 /h). Use the Darcy-Weisbach formula. In USCS Units VD– 12.53 19.35 242 ft>s in V gpm 1pipe ID in inches22 0.408 11,500 19.352 0.408 12.53 ft>s Re 3.5 105 36. 36. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.37 FIGURE 32 Relative roughness and friction factors for new, clean pipes for flow of 60°F (15.6°C) water (Hydraulic Institute Engineering Data Book, Reference 5) (1 meter 39.37 in 3.28 ft). In SI units From Figure 33 From Figure 32 From Figure 31 Using Eq. 16, In USCS units D 19.35 12 1.61 ft f 0.012 D 0.00009 Re 3 106 VD 3.83 0.4915 1.88 m>s m 1.88 129.2 242 ft>s in V m3 >h 1pipe ID in cm2 3.54 2612 49.152 3.54 3.83 m>s 37. 37. 8.38 CHAPTER EIGHT FIGURE 33 Kinematic viscosity and Reynolds number. (Hydraulic Institute Engineering Data Book, Ref.erence 5) [1 ft2 /s 0.0929 m2 /s; 1 cSt 1.0 106 m2 /s; 1VD (m/s m) 129.2 VD" (ft/s in); °F (°C 18) 1.8] 38. 38. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.39 In SI units EXAMPLE 7 The flow in Example 6 is increased until complete turbulence results. Determine the friction factor f and flow. From Figure 31, follow the relative roughness curve e/D 0.00009 to the beginning of the zone marked “complete turbulence, rough pipes” and read The problem may also be solved using Figure 32. Enter relative roughness e/D 0.00009 and read directly across to An increase in Re from 3 106 to 2 107 would require an increase in flow to in USCS units in SI units EXAMPLE 8 The liquid in Example 6 is changed to water at 60°F (15.6°C). Determine Re, f, and the frictional head loss per 100 ft (100 m) of pipe. (as in Example 6) Because the liquid is 60°F (15.6°C) water, enter Figure 31 and read directly down- ward from VD– to Where the line VD– to Re crosses e/D 0.00009 in Figure 31, read Water at 60°F (15.6°C) is more viscous than 109°F (42.8°C) water, and this accounts for the fact that Re decreases and f increases. Using Eq. 16, it can be calculated that the frictional head loss increases to in USCS units in SI units EXAMPLE 9 A 102-in (259-cm) ID welded steel pipe is to be used to convey water at a velocity of 11.9 ft/s (3.63 m/s). Calculate the expected loss of head due to friction per 1000 ft and per 1000 m of pipe after 20 years. Use the empirical Hazen-Williams formula. From Table 2, C 100. In USCS units In SI units r D 4 2.59 4 0.648 m r D 4 102 14 122 2.13 ft hf f L D V2 2g 0.013 100 0.4915 3.832 2 9.807 1.97 m hf f L D V2 2g 0.013 100 1.61 12.532 2 32.17 1.97 ft f 0.013 Re 1.8 106 VD– 242 ft>s in 2 107 3 106 2612 17,413 m3 >h 2 107 3 106 11,500 76,700 gpm f 0.0119 f 0.0119 at Re 2 107 hf f L D V2 2g 0.012 30.48 0.4915 3.832 2 9.807 0.556 m hf f L d V2 2g 0.012 100 1.61 12.532 2 32.17 1.82 ft 39. 39. 8.40 CHAPTER EIGHT FIGURE 34 Nomogram for the solution of the the Hazen-Williams formula. Obtain values for C from Table 2. (Reference 15) (1 m/s 3.28 ft/s; 1 m 39.37 in) Substituting in Eq. 17, in USCS units in SI units The problem may also be solved by using Figure 34, following the trace lines: Frictional Loss for Viscous Liquids Table 3 gives the frictional loss for viscous liq- uids flowing in new Schedule 40 steel pipe. Values of pressure loss are given for both lam- inar and turbulent flows. For laminar flow, the pressure loss is directly proportional to the viscosity and the velocity of flow and inversely proportional to the pipe diameter to the fourth power.There- fore, for intermediate values of viscosity and flow, obtain the pressure loss by direct inter- hf 5 ft 1m2 hf 1000 0.0048 4.8 m S 10.056221>0.54 0.0048 m>m S0.54 V 0.8492Cr0.63 3.63 0.8492 100 0.6480.63 0.0562 hf 1000 0.0048 4.8 ft S 10.055721>0.54 0.0048 ft>ft S0.54 V 1.318Cr0.63 11.9 1.318 100 2.130.63 0.0557 40. 40. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.41 polation. For pipe sizes not shown, multiply the fourth power of the ratio of any tabulated diameter to the pipe diameter wanted by the tabulated loss shown. The flow rate and vis- cosity must be the same for both diameters. For turbulent flow and for rates of flow and pipe sizes not tabulated, the following pro- cedures may be followed. For the viscosity and pipe size required, an intermediate flow loss is found by selecting the pressure loss for the next lower flow and multiplying by the square of the ratio of actual to tabulated flow rates. For the viscosity and flow required, an intermediate pipe diameter flow loss is found by selecting the pressure loss for the next smaller diameter and multiplying by the fifth power of the ratio of tabulated to actual inside diameters. The viscosity of various common liquids can be found in tables in the appendix. Partially Full Pipes and Open Channels Another popular empirical equation applic- able to the flow of water in pipes flowing full or partially full or in open channels is the Manning formula: In USCS units (18a) In SI units (18b) where V average velocity, ft/s (m/s) n friction factor for this formula, which depends on roughness only r hydraulic radius (liquid area divided by wetted perimeter), ft (m) S hydraulic gradient or frictional head loss per unit length of conduit, ft/ft (m/m) The Manning formula nomogram shown in Figure 35 can be used to determine the flow or frictional head loss in open or closed conduits. Note that the hydraulic gradient S in Fig- ure 35 is plotted in feet per 100 ft of conduit length. Values of friction factor n are given in Table 4. If the conduit is flowing partially full, computing the hydraulic radius is sometimes difficult. When the problem to be solved deals with a pipe that is not flowing full, Figure 36 may be used to obtain multipliers for correcting the flow and velocity of a full pipe to the values needed for the actual fill condition. If the flow in a partially full pipe is known and the frictional head loss is to be determined, Figure 36 is first used to correct the flow to what it would be if the pipe were full. Then Eq. 18 or Figure 35 is used to determine the frictional head loss (which is also the hydraulic gradient and the slope of the pipe). The problem is solved in reverse if the hydraulic gradient is known and the flow is to be determined. For full or partially full flow in conduits that are not circular in cross section, an alter- nate solution to using Eq. 18 is to calculate an equivalent diameter equal to four times the hydraulic radius. If the conduit is extremely narrow and width is small relative to length (annular or elongated sections), the hydraulic radius is one-half the width of the section.4 After the equivalent diameter has been determined, the problem may be solved by using the Darcy-Weisbach formula (Eq. 16). The hydraulic gradient in a uniform open channel is synonymous with frictional head loss in a pressure pipe.The hydraulic gradient of an open channel or of a pipe flowing partially full is the slope of the free liquid surface. In the reach of the channel where the flow is uniform, the hydraulic gradient is parallel to the slope of the channel bottom. Figure 37 shows that, in a pressure pipe of uniform cross section, the slope of both the energy and hydraulic gradients is a measure of the frictional head loss per foot (meter) of pipe between points 1 and 2. Figure 38 illustrates the flow in an open channel of varying slope. Between points 1 and 2, the flow is uniform and the liquid surface (hydraulic gradient) and channel bottom are both parallel and their slope is the frictional head loss per foot (meter) of channel length. V r2>3 S1>2 n V 1.486 n r2>3 S1>2 41. 41. TABLE 3 Frictional loss for viscous liquids (Hydraulic Institute Engineering Data Book, Reference 5) Pipe Viscosity, SSU gpm size 100 200 300 400 500 1000 1500 2000 11.2 23.6 35.3 47.1 59 118 177 236 3 3.7 7.6 11.5 15.3 19.1 38.2 57 76 1 1.4 2.9 4.4 5.8 7.3 14.5 21.8 29.1 6.1 12.7 19.1 25.5 31.9 61 96 127 5 1 2.3 4.9 7.3 9.7 12.1 21.2 36.3 48.5 1 0.77 1.6 2.4 3.3 4.1 8.1 12.2 16.2 8.5 17.9 26.8 35.7 44.6 89 134 178 7 1 3.2 6.8 10.2 13.6 17 33.9 51 68 1 1.1 2.3 3.4 4.5 5.7 11.4 17 22.7 1 4.9 9.7 14.5 19.4 24.2 48.5 73 97 10 1 1.6 3.3 4.9 6.5 8.1 16.2 24.3 32.5 1 0.84 1.8 2.6 3.5 4.4 8.8 13.1 17.5 1 11 14.5 21.8 29.1 36.3 73 109 145 15 1 2.8 4.9 7.3 9.7 12.2 24.3 36.5 48.7 1 1.3 2.6 3.9 5.3 6.6 13.1 197 26.3 1 18 18 29.1 38.8 48.5 97 145 194 1 4.9 6.4 9.7 13 16.2 32.5 48.7 65 20 1 2.3 3.5 5.3 7 8.8 17.5 26.3 35 2 0.64 1.3 1.9 2.6 3.2 6.4 9.6 12.9 1 3.5 4.4 6.6 8.8 11 21.9 32.8 43.8 25 2 1 1.6 2.4 3.2 4 8 12.1 16.1 2 0.4 0.79 1.2 1.6 2 4 5.9 7.9 1 5 5.3 7.9 10.5 13.1 26.3 39.4 53 30 2 1.4 1.9 2.9 3.9 4.8 9.6 14.5 19.3 2 0.6 0.95 1.4 1.9 2.4 4.7 7.1 9.5 1 8.5 9 10.5 14 17.5 35 53 70 40 2 2.5 2.5 3.9 5.1 6.4 12.9 19.3 25.7 2 1.1 1.3 1.9 2.5 3.2 6.3 9.5 12.6 1 12.5 14 14 17.5 21.9 43.8 66 88 50 2 3.7 4 4.8 6.4 8 16.1 24.1 32.1 2 1.6 1.7 2.4 3.2 4 7.9 11.8 15.8 2 5 5.8 5.8 7.7 9.6 19.3 28.9 38.5 60 2 2.2 2.4 2.8 3.8 4.7 9.5 14.2 19 3 0.8 0.8 1.2 1.6 2 4 6 8 2 2.8 3.2 3.4 4.4 5.5 11.1 16.6 22.1 70 3 1 1.1 1.4 1.9 2.3 4.6 7 9.3 4 0.27 0.31 0.47 0.63 0.78 1.6 2.4 3.1 2 3.6 4.2 4.2 5.1 6.3 12.6 19 25.3 80 3 1.3 1.4 1.6 2.1 2.7 5.3 8 10.6 4 0.36 0.36 0.54 0.72 0.89 1.8 2.7 3.6 2 5.3 6.1 6.4 6.4 8 15.8 23.7 31.6 100 3 1.9 2.2 2.2 2.7 3.3 6.6 9.9 13.3 4 0.52 0.57 0.67 0.89 1.1 2.2 3.4 4.5 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 4 1 2 1 4 1 2 1 4 1 4 3 4 1 4 3 4 3 4 1 2 8.42 CHAPTER EIGHT TURBULENT FLOW LAMINAR FLOW Loss in pounds per square inch per 100 ft of new Schedule 40 steel pipe based on specific gravity of 1.00 of that liquid. For commercial installations, it is recommended that 15% be added to the values in this table. 42. 42. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.43 LAMINAR FLOW TABLE 3 Continued. Viscosity, SSU 2500 3000 4000 5000 6000 7000 8000 9000 10,000 15,000 294 353 471 589 706 824 942 . . . . . . . . . 96 115 153 191 229 268 306 344 382 573 36.3 43.6 58 73 87 101 116 131 145 218 159 191 255 319 382 446 510 573 637 956 61 73 97 121 145 170 194 218 242 363 20.3 24.3 32.5 40.6 48.7 57 65 73 81 122 223 268 357 416 535 624 713 803 892 . . . 85 102 136 170 203 237 271 305 339 509 28.4 34.1 45.4 57 68 80 91 102 114 170 121 145 194 242 291 339 388 436 485 727 40.6 48.7 65 81 97 114 130 146 162 243 21.9 26.3 35 43.8 53 61 70 79 88 131 182 218 291 363 436 509 581 654 727 . . . 61 73 97 122 146 170 195 219 243 365 32.8 39.4 53 66 79 92 105 118 131 197 242 291 388 485 581 678 775 872 . . . . . . 81 97 130 162 195 227 260 292 325 487 43.8 53 70 88 105 123 140 158 175 263 16.1 19.3 25.7 32.1 38.5 45 51 58 64 96 55 66 88 110 131 153 176 197 219 328 20.1 24.1 32.1 40.2 48.2 56 61 72 80 121 9.9 11.8 15.8 19.7 23.7 27.6 31.6 35.5 39.5 59 66 79 105 131 158 184 210 237 263 394 24.1 28.9 38.5 48.2 58 67 77 87 96 145 11.8 14.2 19 23.7 28.4 33.2 37.9 42.6 47.4 71 88 105 140 175 210 245 280 315 350 526 32.1 38.5 51 64 77 90 103 116 129 193 15.8 19 25.3 31.6 37.9 44.2 51 57 63 95 110 131 175 219 263 307 350 394 438 657 40.2 48.2 64 80 96 112 129 145 161 241 19.7 23.7 31.6 39.5 47.4 55 63 71 79 118 48.2 58 77 96 116 135 154 173 193 289 23.7 28.4 37.9 47.4 57 66 76 85 95 142 9.9 11.9 15.9 19.9 23.9 27.9 31.8 35.8 39.8 60 27.6 33.2 44.2 55 66 77 88 100 111 166 11.6 13.9 18.6 23.2 27.8 32.5 37.1 41.7 46.4 70 3.9 4.7 6.3 7.8 9.4 11 12.5 14.1 15.6 23.5 31.6 37.9 51 63 76 88 101 114 126 190 13.3 15.9 21.2 26.5 31.8 37.1 42.4 47.7 53 80 4.5 5.4 7.2 8.9 10.7 12.5 14.3 16.1 17.9 26.8 39.5 47.4 63 79 95 111 127 142 158 237 16.6 19.9 26.5 33.1 39.8 46.4 53 60 66 99 5.6 6.7 8.9 11.2 13.4 15.6 17.9 20.1 22.3 33.5 For a liquid having a specific gravity other than 1.00, mulitply the value from the table by the specific gravity. No allowance for aging of pipe is included. 43. 43. TABLE 3 Continued. Pipe Viscosity, SSU gpm size 100 200 300 400 500 1000 1500 2000 3 2.7 3.1 3.2 3.2 4 8 11.9 15.9 120 4 0.73 0.81 0.81 1.1 1.3 2.7 4 5.4 6 0.98 0.11 0.16 0.21 0.26 0.52 0.78 1.0 3 3.4 4 4.3 4.3 4.6 9.3 13.9 18.6 140 4 0.95 1.1 1.1 1.3 1.6 3.1 4.7 6.3 6 0.17 0.18 0.21 0.28 0.35 0.69 1.0 1.4 3 4.4 5 5.7 5.7 5.7 10.6 15.9 21.2 160 4 1.2 1.4 1.4 1.4 1.8 3.6 5.4 7.2 6 0.17 0.18 0.21 0.28 0.35 0.69 1.0 1.4 3 5.3 6.3 7 7 7 11.9 17.9 23.9 180 4 1.5 1.8 1.8 1.8 2 4 6 8 6 0.2 0.24 0.24 0.31 0.39 0.78 1.2 1.6 3 6.5 7.7 8.8 8.8 8.8 13.3 19.9 26.5 200 4 1.8 2.2 2.2 2.2 2.2 4.5 6.7 8.9 6 0.25 0.3 0.3 0.35 0.43 0.87 1.3 1.7 4 2.6 3.2 3.5 3.5 3.5 5.6 8.4 11.2 250 6 0.36 0.43 0.45 0.45 0.51 1.1 1.6 2.2 8 0.95 0.12 0.12 0.15 0.18 0.36 0.54 0.72 4 3.7 4.3 5 5 5 6.7 10.1 13.4 300 6 0.5 0.6 0.65 0.65 0.65 1.3 2 2.6 8 0.13 0.17 0.17 0.18 0.22 0.43 0.65 0.87 6 0.82 1 1.1 1.2 1.2 1.7 2.6 3.5 400 8 0.23 0.27 0.29 0.29 0.29 0.58 0.87 1.2 10 0.08 0.09 0.1 0.1 0.12 0.23 0.35 0.47 6 1.2 1.5 1.6 1.8 1.8 2.2 3.2 4.3 500 8 0.33 0.39 0.44 0.47 0.47 0.72 1.1 1.5 10 0.11 0.14 0.15 0.15 0.15 0.29 0.44 0.58 6 1.8 2.2 2.3 2.4 2.6 2.7 3.9 5.2 600 8 0.47 0.57 0.62 0.67 0.67 0.87 1.3 1.7 10 0.16 0.18 0.2 0.22 0.22 0.35 0.52 0.07 6 2.3 2.7 3 3.2 3.5 3.6 4.6 6.1 700 8 0.6 0.74 0.82 0.89 0.93 1 1.5 2 10 0.2 0.25 0.27 0.3 0.3 0.41 0.61 0.82 6 2.8 3.5 3.7 4 4.2 4.8 5.2 6.9 800 8 0.78 0.94 1 1.1 1.2 1.2 1.7 2.3 10 0.26 0.3 0.34 0.38 0.4 0.47 0.7 0.92 6 3.5 4.3 4.6 5.0 5.2 6 6 7.8 900 8 0.95 1.1 1.3 1.4 1.5 1.5 2 2.6 10 0.32 0.37 0.43 0.46 0.5 0.52 0.79 1.1 8 1.1 1.4 1.5 1.6 1.8 1.9 2.2 2.9 1000 10 0.38 0.45 0.5 0.55 0.6 0.6 0.87 1.2 12 0.17 0.2 0.22 0.24 0.25 0.29 0.43 0.58 8.44 CHAPTER EIGHT TURBULENT FLOW LAMINAR FLOW 44. 44. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.45 TABLE 3 Continued. Viscosity, SSU 2500 3000 4000 5000 6000 7000 8000 9000 10,000 15,000 19.9 23.9 31.8 39.8 47.7 56 61 72 80 119 6.7 8 10.7 13.4 16.1 18.8 21.4 24.1 26.8 40.2 1.3 1.6 2.1 2.6 3.1 3.6 1.2 4.7 5.2 7.8 23.2 27.8 37.1 46.4 56 65 74 84 93 139 7.8 9.4 12.5 15.6 18.8 21.9 25 28.2 31.3 46.9 1.5 1.8 2.4 3.0 3.6 4.2 4.9 5.5 6.0 9.1 26.5 31.8 42.4 53 64 74 85 95 106 159 8.9 10.7 14.3 17.9 21.5 25 28.6 32.2 35.7 54 1.7 2.1 2.8 3.5 4.2 4.9 5.5 6.2 6.9 10.4 29.8 35.8 47.7 60 72 84 95 107 119 179 10.1 12.1 16.1 20.1 24.1 28.1 32.2 36.2 40.2 60 2 2.3 3.1 3.9 4.7 5.5 6.2 7 7.8 11.7 33.1 39.8 53 66 80 93 106 119 133 199 11.2 13.4 17.9 22.3 26.8 31.3 35.7 40.2 44.7 67 2.2 2.6 3.5 4.3 5.2 6.1 6.9 7.8 8.7 13 14 16.8 22.3 27.9 33.5 39.1 44.7 50 56 84 2.7 3.3 4.3 5.4 6.5 7.6 8.7 9.8 10.8 16.3 0.9 1.1 1.5 1.8 2.2 2.5 2.9 3.3 3.6 5.4 16.8 20.1 26.8 33.5 40.2 47 54 60 67 101 3.3 3.9 5.2 6.5 7.8 9.1 10.4 11.7 13 19.5 1.0 1.3 1.7 2.2 2.6 3 3.5 3.9 4.3 6.5 4.3 5.2 6.9 8.7 10.4 12.1 13.9 15.6 17.3 26 1.5 1.7 2.3 2.9 3.5 4.1 4.6 5.2 5.8 8.7 0.58 0.7 0.93 1.2 1.4 1.6 1.9 2.1 2.3 3.5 5.4 6.5 8.7 10.8 13 15.2 17.3 19.5 21.7 32.5 1.8 2.2 2.9 3.6 4.3 5.1 5.8 6.5 7.2 10.8 0.73 0.87 1.2 1.5 1.8 2 2.3 2.6 2.9 4.4 6.5 7.8 10.4 13 16 18.2 20.8 23.4 26 39 2.2 2.6 3.5 4.3 5.2 6.1 6.9 7.8 8.7 13 0.87 1.1 1.4 1.8 2.1 2.4 2.8 3.3 3.5 5.2 7.6 9.1 12.1 15.2 18.4 21.2 24.3 27.3 30.3 45.5 2.5 3 4.1 5.1 6.1 7.1 8.1 9.1 10.1 15.2 1 1.2 1.6 2 2.4 2.9 3.3 3.7 4.1 6.1 8.7 10.4 13.9 17.3 20.8 24.3 27.7 31.2 34.7 52 2.9 3.5 4.6 5.8 6.9 8.1 9.3 10.4 11.6 17.3 1.2 1.4 1.9 2.3 2.8 3.3 3.7 4.2 4.7 7 9.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 39 58.5 3.3 3.9 5.2 6.5 7.8 9.1 10.4 11.7 13 19.5 1.3 1.6 2.1 2.6 3.1 3.7 4.2 4.7 5.2 7.9 3.6 4.3 5.8 7.2 8.7 10.1 11.6 13 14.5 21.7 1.5 1.8 2.3 2.9 3.5 4.1 4.7 5.2 5.8 8.7 0.72 0.87 1.2 1.5 1.7 2 2.3 2.6 2.9 4.3 LAMINAR FLOW 45. 45. TABLE 3 Continued. Pipe Viscosity, SSU gpm size 20,000 25,000 30,000 40,000 50,000 60,000 2 19.3 24.1 28.9 38.5 48.2 58 3 2 9.5 11.8 14.2 19 23.7 28.4 3 4 5 6 8 9.9 11.9 2 32 40 48.2 64 80 96 5 2 15.8 19.7 23.7 31.6 39.5 47.4 3 6.6 8.3 9.9 13.3 16.6 9.9 2 45 56 67 90 112 135 7 2 22.1 27.6 33.2 44.2 55 66 3 9.3 10.6 13.9 18.6 23.2 27.8 2 31.6 39.5 47.4 63 79 95 10 3 13.3 16.6 19.9 26.5 33.1 39.8 4 4.5 5.6 6.7 8.9 11.2 13.4 2 47.4 59 71 95 118 142 15 3 19.9 24.9 29.8 39.8 49.7 60 4 6.7 8.4 10.1 13.4 16.8 20.1 3 26.5 33.1 39.8 53 66 80 20 4 8.9 11.2 13.4 17.9 22.3 26.8 6 1.7 2.2 2.6 3.5 4.3 5.2 3 33.1 41.4 49.7 66 83 99 25 4 11.2 14 16.8 22.3 27.9 33.5 6 2.2 2.7 3.3 4.3 5.4 6.5 3 39.8 49.7 60 80 99 119 30 4 13.4 16.8 20.1 26.8 33.5 40.2 6 2.6 3.3 3.9 5.2 6.5 7.8 3 53 66 80 106 133 160 40 4 17.9 22.3 26.8 35.7 44.7 54 6 3.5 4.3 5.2 6.9 8.7 10.4 4 22.3 27.9 33.5 44.7 56 67 50 6 4.3 5.4 6.5 8.7 10.8 13 8 1.5 1.8 2.7 2.9 3.6 4.3 4 26.8 33.5 40.2 54 67 80 60 6 5.2 6.5 7.8 10.4 13 16 8 1.7 2.2 2.6 3.5 4.3 5.2 4 31.3 39.1 46.9 63 78 94 70 6 6.1 7.6 9.1 12.1 15.2 18.4 8 2 2.5 3 4.1 5.1 6.1 6 6.9 8.7 10.4 13.9 17.3 20.8 80 8 2.3 2.9 3.5 4.6 5.8 6.9 10 0.93 1.2 1.4 1.9 2.3 2.8 6 7.8 9.8 11.7 15.6 19.5 23.4 90 8 2.6 3.3 3.9 5.2 6.5 7.8 10 1.1 1.3 1.6 2.1 2.6 3.1 1 2 1 2 1 2 1 2 1 2 8.46 CHAPTER EIGHT LAMINAR FLOW 46. 46. 8.1 PUMPING SYSTEMS AND SYSTEM-HEAD CURRVES 8.47 TABLE 3 Continued. Viscosity, SSU 70,000 80,000 90,000 100,000 125,000 150,000 175,000 200,000 500,000 67 77 87 96 120 145 169 193 482 332 37.9 42.6 47.4 59 71 83 95 237 13.9 15.9 17.9 19.9 24.9 29.8 34.8 39.8 99 112 129 145 161 200 241 281 321 803 55 63 71 79 99 118 138 158 395 23.2 26.5 29.8 33 41.4 49.7 58 66 166 157 180 202 225 281 337 393 450 . . . 77 88 100 111 138 166 194 221 553 32.5 37.1 40.7 46.4 58 70 81 93 232 111 126 142 158 197 237 276 316 790 46.4 53 60 66 83 99 116 133 331 15.6 17.9 20.1 22.3 27.9 33.5 39.1 44.7 112 166 190 213 237 296 355 415 474 . . . 70 80 89 99 124 149 174 199 497 23.5 26.8 30.2 33.5 41.9 50 59 67 168 93 106 119 133 166 199 232 265 663 31.3 35.7 40.2 44.7 56 67 78 89 223 6.1 6.9 7.8 8.7 10.8 13 15.2 17.3 43.3 116 133 149 166 207 49 290 331 828 39.1 44.7 50 56 70 84 98 112 279 7.6 8.7 9.8 10.8 13.5 16.3 19 21.7 54 139 159 179 199 249 298 348 398 . . . 46.9 54 60 67 84 101 117 134 335 9.1 10.4 11.7 13 16.3 19.5 22.7 26 65 186 212 239 265 331 398 464 532 . . . 63 72 80 89 112 134 156 179 447 12.1 13.9 15.6 17.3 21.7 26 30.3 34.7 87 78 89 101 112 140 168 196 223 559 15.2 17.3 19.5 21.7 27.1 32.5 37.9 43.3 107 5.1 5.8 6.5 7.2 9 10.8 12.6 14.5 36.1 94 107 121 134 168 201 235 268 670 18.2 20.8 23.4 26 32.5 39 45.5 52 130 6.1 6.9 7.8 8.7 10.8 13 15.2 17.3 43.4 110 125 141 156 196 235 274 313 782 21.2 24.3 27.3 30.3 37.9 45.5 53 61 152 7.1 8.1 9.1 10.1 12.6 15.2 17.7 20.2 51 24.3 27.7 31.2 34.7 43.3 52 61 69 173 8.1 9.3 10.4 11.6 14.5 17.3 20.2 23.1 58 3.3 3.7 4.2 4.7 5.8 7 8.2 9.3 23.3 27.3 31.2 35.1 39 48.7 59 68 78 195 9.1 10.4 11.7 13 16.3 19.5 22.8 26 65 3.7 4.2 4.7 5.2 6.6 7.9 9.2 10.5 26.2 LAMINAR FLOW 47. 47. TABLE 3 Continued. Pipe Viscosity, SSU gpm size 20,000 25,000 30,000 40,000 50,000 60,000 6 8.7 10.8 13 17.3 21.7 26 100 8 2.9 3.6 4.3 5.8 7.2 8.7 10 1.2 1.5 1.8 2.3 2.9 3.5 6 10.4 13 15.6 20.8 26 31.2 120 8 3.5 4.3 5.2 6.9 8.7 10.4 10 1.4 1.8 2.1 2.8 3.5 4.2 6 12.1 15.2 18.2 24.3 30.3 36.4 140 8 4 5.1 6.1 8.1 10.1 12.1 10 1.7 2 2.4 3.3 4.1 4.9 6 13.9 17.3 20.8 27.7 34.7 41.6 160 8 4.6 5.8 6.9 9.3 11.6 13.8 10 1.9 2.3 2.8 3.7 4.7 5.6 6 15.6 19.5 23.4 31.2 39 46.8 180 8 5.2 6.5 7.8 10.4 13 15.6 10 2.1 2.6 3.1 4.2 5.2 6.3 8 5.8 7.2 8.7 11.6 14.5 17.3 200 10 2.3 2.9 3.5 4.7 5.8 7 12 1.2 1.5 1.7 2.3 2.9 3.5 8 7.2 9 10.8 14.5 18.1 21.7 250 10 2.9 3.6 4.4 5.8 7.3 8.7 12 1.5 1.8 2.2 2.9 3.6 4.3 8 8.7 10.8 13 17.3 21.7 26 300 10 3.5 4.4 5.2 7 8.7 10.5 12 1.7 2.2 2.6 3.5 4.3 5.2 8 11.6 14.5 17.3 23 28.9 34.7 400 10 4.7 5.8 7 9.3 11.6 14 12 2.3 2.9 3.5 4.6 5.8 7 8 14.5 18.1 21.7 28.9 36.1 43.4 500 10 5.8 7.3 8.7 11.6 14.6 17.5 12 2.9 3.6 4.3 5.8 7.2 8.7 8 17.3 21.7 26 34.7 43.4 52 600 10 7 8.7 10.5 14 17.5 21 12 3.5 4.3 5.2 7 8.7 10.4 8 20.2 25.3 30.3 40.5 51 61 700 10 8.2 10.2 12.2 16.3 20.4 24.4 12 4.1 5.1 6.1 8.1 10.1 12.2 8 23.1 28.9 34.7 46.2 58 69 800 10 9.3 11.6 14 18.6 23.3 27.9 12 4.6 5.8 7 9.3 11.6 13.9 8 26 32.5 39 52 65 78 900 10 10.5 13.1 15.7 21 26.2 31.4 12 5.2 6.5 7.8 10.4 13 15.6 8 28.9 36.1 43.4 58 72 87 1000 10 11.6 14.6 17.5 23.3 29.1 34.9 12 5.8 7.2 8.7 11.6 14.5 17.4 8.48 CHAPTER EIGHT LAMINAR FLOW

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