Standard Methods for Examination of Water & Wastewater_3 potx

249_frame_CH-04 Page 211 Friday, June 14, 2002 4:25 PM Pumping Pumping is a unit operation that is used to move fluid from one point to another This chapter discusses various topics of this important unit operation relevant to the physical treatment of water and wastewater These topics include pumping stations and various types of pumps; total developed head; pump scaling laws; pump characteristics; best operating efficiency; pump specific speed; pumping station heads; net positive suction head and deep-well pumps; and pumping station head analysis 4.1 PUMPING STATIONS AND TYPES OF PUMPS The location where pumps are installed is a pumping station There may be only one pump, or several pumps Depending on the desired results, the pumps may be connected in parallel or in series In parallel connection, the discharges of all the pumps are combined into one Thus, pumps connected in parallel increases the discharge from the pumping station On the other hand, in series connection, the discharge of the first pump becomes the input of the second pump, and the discharge of the second pump becomes the input of the third pump and so on Clearly, in this mode of operation, the head built up by the first pump is added to the head built up by the second pump, and the head built up by the second pump is added to the head built by the third pump and so on to obtain the total head developed in the system Thus, pumps connected in series increase the total head output from a pumping station by adding the heads of all pumps Although the total head output is increased, the total output discharge from the whole assembly is just the same input to the first pump Figure 4.1 shows section and plan views of a sewage pumping station, indicating the parallel type of connection The discharges from each of the three pumps are conveyed into a common manifold pipe In the manifold, the discharges are added As indicated in the drawing, a manifold pipe has one or more pipes connected to it Figure 4.2 shows a schematic of pumps connected in series As indicated, the discharge flow introduced into the first pump is the same discharge flow coming out of the last pump The word pump is a general term used to designate the unit used to move a fluid from one point to another The fluid may be contaminated by air conveying fugitive dusts or water conveying sludge solids Pumps are separated into two general classes: the centrifugal and the positive-displacement pumps Centrifugal pumps are those that move fluids by imparting the tangential force of a rotating blade called an impeller to the fluid The motion of the fluid is a result of the indirect action of the impeller Displacement pumps, on the other hand, literally push the fluid in order to move it Thus, the action is direct, positively moving the fluid, thus the name positive-displacement pumps In centrifugal pumps, flows are introduced into the © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 212 Friday, June 14, 2002 4:25 PM Reflux valve Automatic Motor starter Float tube A A Suction well T W L Float tube Centrifugal pumps Sluice valve Sluice valve Screen Section A-A Sewer Sectional plan Rising main FIGURE 4.1 Plan and section of a pumping station showing parallel connections Q out Impeller eye Q in FIGURE 4.2 Pumps connected in series unit through the eye of the impeller This is indicated in Figure 4.2 where the “Q in” line meets the “eye.” In positive-displacement pumps, no eye exists The left-hand side of Figure 4.3 shows an example of a positive-displacement pump Note that the screw pump literally pushes the wastewater in order to move it The right-hand side shows a cutaway view of a deep-well pump This pump is a centrifugal pump having two impellers connected in series through a single shaft forming a two-stage arrangement Thus, the head developed by the first stage is added to that of the second stage producing a much larger head developed for the whole assembly As discussed later in this chapter, this series type of connection is necessary for deep wells, because there is a limit to the depth that a single pump can handle Figure 4.4 shows various types of impellers that are used in centrifugal pumps The one in a is used for axial-flow pump Axial-flow pumps are pumps that transmit the fluid pumped in the axial direction They are also called propeller pumps, because the impeller simply propels the fluid forward like the movement of a ship with propellers The impeller in d has a shroud or cover over it This kind of design can develop more © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 213 Friday, June 14, 2002 4:25 PM 213 Screw pumps Second stage Impeller First stage FIGURE 4.3 A screw pump, an example of a positive-displacement pump (left); cutaway view of a deep-well pump (right) (a) (b) Shroud (c) (d) FIGURE 4.4 Various types of pump impellers: (a) axial flow; (b) open type; (c) mix-flow type; and (d) shrouded impeller © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 214 Friday, June 14, 2002 4:25 PM head as compared to the one without a shroud The disadvantage, however, is that it is not suited for pumping liquids containing solids in it, such as rugs, stone, and the like, because these materials may easily clog the impeller In general, a centrifugal impeller can discharge its flow in three ways: by directly throwing the flow radially into the side of the chamber circumscribing it, by conveying the flow forward by proper design of the impeller, and by a mix of forward and radial throw of the flow The pump that uses the first impeller is called a radialflow pump; the second, as mentioned previously, is called the axial-flow pump; and the third pump that uses the third type of impeller is called a mixed-flow pump The impeller in c is used for mixed-flow pumps Figure 4.5 shows various impellers used for positive-displacement pumps and for centrifugal pumps The figures in d and e are used for centrifugal pumps The figure in e shows the impeller throwing its flow into a discharge chamber that circumscribes a circular geometry as a result of the impeller rotating This chamber is shaped like a spiral and is expanding in cross section as the flow moves into the outlet of the pump Because it is shaped into a spiral, this expanding chamber is called a volute—another word for spiral In centrifugal pumps, the kinetic energy that the flow possesses while in the confines of the impeller is transformed into pressure energy when discharged into the volute This progressive expansion of the cross section of the volute helps in transforming the kinetic energy into pressure energy without much loss of energy Using diffusers to guide the flow as it exits Internal Outlet seal here Motor Shaft Inlet Inlet Outlet Outlet Internal Casing seal here (a) Vanes Inlet (b) (c) Stationary diffuser Diffuser Impeller Volute Inlet Outlet Internal seal formed Impeller (d) (e) here (f) FIGURE 4.5 Various types of pump impellers, continued: (a) lobe type; (b) internal gear type; (c) vane type; (d) impeller with stationary guiding diffuser vanes; (e) impeller with volute discharge; and (f) external gear type impeller © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 215 Friday, June 14, 2002 4:25 PM 215 from the tip of the impeller into the volute is another way of avoiding loss of energy This type of design is indicated in d, showing stationary diffusers as the guide The figure in a is a lobe pump, which uses the lobe impeller A lobe pump is a positive-displacement pump As indicated, there is a pair of lobes, each one having three lobes; thus, this is a three-lobe pump The turning of the pair is synchronized using external gearings The clearance between lobes is only a few thousandths of a centimeter, thus only a small amount of leakage passes the lobes As the pair turns, the water is trapped in the “concavity” between two adjacent lobes and along with the side of the casing is positively moved forward into the outlet The figures in b and f are gear pumps They basically operate on the same principle as the lobe pumps, except that the “lobes” are many, which, actually, are now called gears Adjacent gear teeth traps the water which, then, along with the side of the casing, moves the water to the outlet The gear pump in b is an internal gear pump, so called because a smaller gear rolls around the inside of a larger gear (The smaller gear is internal and inside the larger gear.) As the smaller gear rolls, the larger gear also rolls dragging with it the water trapped between its teeth The smaller gear also traps water between its teeth and carries it over to the crescent The smaller and the larger gears eventually throw their trapped waters into the discharge outlet The gear pump in f is an external gear pump, because the two gears are contacting each other at their peripheries (external) The pump in c is called a vane pump, so called because a vane pushes the water forward as it is being trapped between the vane and the side of the casing The vane pushes firmly against the casing side, preventing leakage back into the inlet A rotor, as indicated in the figure, turns the vane Fluid machines that turn or tend to turn about an axis are called turbomachines Thus, centrifugal pumps are turbomachines Other examples of turbomachines are turbines, lawn sprinklers, ceiling fans, lawn mower blades, and turbine engines The blower used to exhaust contaminated air in waste-air works is a turbomachine 4.2 PUMPING STATION HEADS In the design of pumping stations, the engineer must ensure that the pumping system can deliver the fluid to the desired height For this reason, energies are conveniently expressed in terms of heights or heads The various terminologies of heads are defined in Figure 4.6 Note that two pumping systems are portrayed in the figure: pumps connected in series and pumps connected in parallel Also, two sources of the water are pumped: the first is the source tank above the elevation of the eye of the impeller or centerline of the pump system; the second is the source tank below the eye of the impeller or centerline of the pump system The flow in flow pipes for the first case is shown by dashed lines In addition, the pumps used in this pumping station are of the centrifugal type The terms suction and discharge in the context of heads refer to portions of the system before and after the pumping station, respectively Static suction lift hᐉ is the vertical distance from the elevation of the inflow liquid level below the pump inlet to the elevation of the pump centerline or eye of the impeller A lift is a negative head Static suction head hs is the vertical distance from the elevation of the inflow liquid level above the pump inlet to the elevation of the pump centerline Static discharge head hd is the vertical distance from the centerline elevation of the pump © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 216 Friday, June 14, 2002 4:25 PM Pumping station B h st A hd c b d a hd hs i hᐉ hd hd k hst hᐉ f e j h g hs Pump centerline Pumping station FIGURE 4.6 Pumping station heads to the elevation of the discharge liquid level Total static head hst is the vertical distance from the elevation of the inflow liquid level to the elevation of the discharge liquid level Suction velocity head hvs is the entering velocity head at the suction side of the pump hydraulic system This is not the velocity head at the inlet to a pump such as points a, c, e, etc in the figure In the figure, because the velocity in the wet well is practically zero, hvs will also be practically zero Discharge velocity head hvd is the outgoing velocity head at the discharge side of the pump hydraulic system Again, this is not the velocity head at the discharge end of any particular pump In the figure, it is the velocity head at the water level in the discharge tank, which is also practically zero 4.2.1 TOTAL DEVELOPED HEAD The literature has used two names for this subject: total dynamic head or total developed head (H or TDH) Let us derive TDH first by considering the system connected in parallel between points and Since the connection is parallel, the head losses across each of the pumps are equal and the head given to the fluid in each of the pumps are also equal Thus, for our analysis, let us choose any pump such as the one with inlet g From fluid mechanics, the energy equation between the points is 2 P1 V P V2 + - + z – h f + h q + h p = + - + z γ 2g γ 2g (4.1) where P, V, and z are the pressure, velocity, and elevation head at the indicated points; g is the acceleration due to gravity; hf is the head equivalent of the resistance loss (friction) between the points; hq is the head equivalent of the heat added to the flow; © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 217 Friday, June 14, 2002 4:25 PM 217 and hp is the head given to the fluid by the pump impeller Using the level at point as the reference datum, z1 equals zero and z2 equals hst It is practically certain that there will be no hq in the physical–chemical treatment of water and wastewater, and will therefore be neglected Let hf be composed of the head loss inside the pump hlp, plus the head loss in the suction side of the pumping system hfs and the head loss in the discharge side of the pumping system hfd Thus, the energy equation becomes 2 P1 V P V2 + - – h lp – h fs – h fd + h p = + - + h st γ 2g γ 2g (4.2) The equation may now be solved for −hlp + hp This term is composed of the head added to the fluid by the pump impeller, hp, and the losses expended by the fluid inside the pump, hlp As soon as the fluid gets the hp, part of this will have to be expended to overcome frictional resistance inside the pump casing The fluid that is actually receiving the energy will drag along those that are not This dragging along is brought about because of the inherent viscosity that any fluid possesses The process causes slippage among fluid planes, resulting in friction and turbulent mixing This friction and turbulent mixing is the hlp The net result is that between the inlet and the outlet of the pump is a head that has been developed This head is called the total developed head or total dynamic head (TDH) and is equal to −hlp + hp Solving Equation (4.2) for −hlp + hp, considering that the tanks are open to the atmosphere and that the velocities at points and at the surfaces are practically zero, produces TDH = TDH0sd = – h lp + h p = h st + h fs + h fd (4.3) When the two tanks are open to the atmosphere, P1 and P2 are equal; they, therefore, cancel out of the equation Thus, as shown in the equation, TDH is referred to as TDH0sd In this designation, stands for the fact that the pressures cancel out The s and d signify that the suction and discharge losses are used in calculating TDH The sum hfs + hfd may be computed as the loss due to friction in straight runs of pipe, hfr , and the minor losses of transitions and fittings, hfm Thus, calling the corresponding TDH as TDH0rm (rm for run and minor, respectively), TDH = TDH0rm = – h lp + h p = h st + h fr + h fm (4.4) From fluid mechanics, l V h fr = f  -   -   D  2g (4.5) V h fm = K  -   2g © 2003 by A P Sincero and G A Sincero (4.6) 249_frame_CH-04 Page 218 Friday, June 14, 2002 4:25 PM where f is Fanning’s friction factor, l is the length of the pipe, D is the diameter of the pipe, V is the velocity through the pipe, g is the acceleration due to gravity 2 (equals 9.81 m/s ) and K is the head loss coefficient V /2g is called the velocity head, hv That is, V h v = 2g (4.7) If the points of application of the energy equation is between points and B, instead of between points and 2, the pressure terms and the velocity heads will remain intact at point B In this situation, refering to the TDH as TDHfullsd ( full because velocities and pressure are not zeroed out), P B – P atm V B TDH = TDHfullsd = – h lp + h p = + - + z + h fs + h fd γ 2g (4.8) where z2 is the elevational head of point B, referred to the chosen datum at point Note that Patm is the pressure at point 1, the atmospheric pressure When the friction losses are expressed in terms of hfr + hfm and calling the TDH as TDH fullrm, the equation is P B – P atm V B TDH = TDHfullrm = – h lp + h p = + - + z + h fr + h fm γ 2g (4.9) If the energy equation is applied using the source tank at the upper elevation as point 1, the same respective previous equations will also be obtained In addition, if the energy equation is applied to the system of pumps that are connected in series, the same equations will be produced except that TDH will be the sum of the TDHs of the pumps in series Also the subscripts denoted by B will be changed to A See Figure 4.6 4.2.2 INLET AND OUTLET MANOMETRIC HEADS; INLET AND OUTLET DYNAMIC HEADS Applying the energy equation between an inlet i and outlet o of any pump produces 2 P Vo P Vi TDH = TDHmano = – h lp + h p =  o + -  –  i + -   γ 2g  γ 2g (4.10) where TDHmano (mano for manometric) is the name given to this TDH hfs + hfd is equal to zero P i / γ = h i is called either the inlet manometric head or the inlet © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 219 Friday, June 14, 2002 4:25 PM manometric height absolute; P o /γ = h o is also called either the outlet manometric head or the outlet manometric height absolute The subscripts i and o denote “inlet” and “outlet,” respectively Manometric head or level is the height to which the liquid will rise when subjected to the value of the gage pressure; on the other hand, manometric height absolute is the height to which the liquid will rise when subjected to the true or absolute pressure in a vacuum environment The liquid rising that results in the manometric head is under a gage pressure environment, which means that the liquid is exposed to the atmosphere The liquid rising, on the other hand, that results in the manometric height absolute is not exposed to the atmosphere but under a complete vacuum Retain h as the symbol for manometric head and, for specificity, use habs as the symbol for manometric height absolute Thus, the respective formulas are P h = g γ P h abs = -γ (4.11) (4.12) Pg is the gage pressure and P is the absolute pressure Unless otherwise specified, P is always the absolute pressure 2 In terms of the new variables and the velocity heads V i /2g = hvi and V i /2g = hvo for the pump inlet and outlet velocity heads, respectively, TDH, designated as TDHabs, may also be expressed as TDH abs = h abso + h vo – ( h absi + h vi ) (4.13) Note that habs is used rather than h h is merely a relative value and would be a mistake if substituted into the above equation For static suction lift conditions, hi is always negative since gage pressure is used to express its corresponding pressure, and its theoretical limit is the negative of the difference between the prevailing atmospheric pressure and the vapor pressure of the liquid being pumped If the pressure is expressed in terms of absolute pressure, then habs has as its theoretical limit the vapor pressure of the liquid being pumped Because of the suction action of the impeller and because the fluid is being lifted, the fluid column becomes “rubber-banded.” Just like a rubber band, it becomes stretched as the pressure due to suction is progressively reduced; eventually, the liquid column ruptures As the rupture occurs, the inlet suction pressure will actually have gone down to equal the vapor pressure, thus, vaporizing the liquid and forming bubbles This process is called cavitation Cavitation can destroy hydraulic structures As the bubbles which have been formed at a partial vacuum at the inlet gradually progress along the impeller toward the outlet, the sudden increase in pressure causes an impact force Continuous action of this force shortens the life of the impeller © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 220 Friday, June 14, 2002 4:25 PM The sum of the inlet manometric height absolute and the inlet velocity head is called the inlet dynamic head, idh (dynamic because this value is obtained with fluid in motion) The sum of the outlet manometric height absolute and the outlet velocity head is called the outlet dynamic head, odh Of course, the TDH is also equal to the outlet dynamic head minus the inlet dynamic head TDH = TDHdh = odh – idh (4.14) In general, dynamic head, dh is P V dh = + γ 2g (4.15) It should be noted that the correct substitution for the pressure terms in the above equations is always the absolute pressure Physical laws follow the natural measures of the parameters Absolute pressures, absolute temperatures, and the like are natural measures of these parameters Gage pressures and the temperature measurements of Celsius and Fahrenheit are expedient or relative measures This is unfortunate, since oftentimes, it causes too much confusion; however, these relative measures have their own use, and how they are used must be fully understood, and the results of the calculations resulting from their use should be correctly interpreted If confusion results, it is much better to use the absolute measures Example 4.1 It is desired to pump a wastewater to an elevation of 30 m above a sump Friction losses and velocity at the discharge side of the pump system are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1200 rpm Suction friction loss is 1.03 m; the diameter of the suction and discharge lines are 250 and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m (a) If the temperature is 20°C, has cavitation occurred? (b) What are the inlet and outlet manometric heads? (c) What are the inlet and outlet total dynamic heads? From the values of the idh and odh, calculate TDH Solution: (a) P V2 P V1 - + z + + h q – h f + h p = - + z + 2g γ 2g γ Let the sump pool level be point and the inlet to the pump as point A d = cross-section of discharge pipe = πD = π ( 0.225 ) = 0.040 m Therefore, Q = discharge = 1.3 ( 0.040 ) = 0.052 m /s π ( 0.25 ) A = = 0.049 m ; 0.052 V = = 1.059 m/s 0.049 P 1.059 Therefore, + + + – 1.03 + = - + + 2 ( 9.81 ) γ © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 228 Friday, June 14, 2002 4:25 PM For pumps of constant rotational or stroking speed, ω, but of different diameter or stroke, D, the following simplified scaling laws are also obtained: Db H b = - H a Da (4.39) Db Q b = - Q a Da (4.40) Db P b = - P a Da (4.41) Db P brakeb = - P brakea Da (4.42) Example 4.3 For the pump represented by Figure 4.8, determine (a) the discharge when the pump is operating at a head of 10 m and at a speed of 875 rpm, and (b) the efficiency and the brake power Solution: (a) From the figure, Q = 0.17 m /s Ans (b) η = 63% Ans Pbrake = 26 kW Ans Example 4.4 If the pump in Example 4.3 is operated at 1,170 rpm, calculate the resulting H, Q, Pbrake , and η Solution:  Hg   Hg  H ag H bg  1170-   =   ⇒ = ⇒ H b = 10  - = 17.88 m Ans 2 2 2 2 ωb D ωa D 875  ω D b  ω D a  Q   Q  Qb Qa  1170   =   ⇒ = ⇒ Q b = 0.17  - = 0.23 m /s Ans 3 3 875 ωb D ωa D  ω D b  ω D a  P brake   P brake  P brakeb P brakea  -5  =  -5  ⇒ -5 = -5 ⇒ P brakeb 3 3 ρω D b ρω D a ρω b D ρω a D   1170 = 26  - = 62.16 kW Ans  875  η = 63% Ans Example 4.5 If a homologous 30-cm pump is to be used for the problem in Example 4.4, calculate the resulting H, Q, Pbrake , and η for the same rpm © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 229 Friday, June 14, 2002 4:25 PM Solution: The diameter of the pump represented by Figure 4.8 is 375 mm  Hg   Hg  H bg H ag  30 -   =   ⇒ = ⇒ H b = 17.88  -  = 11.44 m Ans 2 2 2 2 ω Db ω Da 37.5  ω D b  ω D a  Q   Q  Qb Qa  30 -   =   ⇒ = ⇒ Q b = 0.23  -  = 0.12 m /s Ans 3 3 ω Db ω Da 37.5  ω D b  ω D a  P brake   P brake  P brakeb P brakeb  -5  =  -5  ⇒ -5 = -5 ⇒ P brakeb 3 3 ρω D b ρω D a  ρω D b  ρω D a 30 = 62.16  -  = 20.37 kW Ans  37.5 5 η = 63% Ans 4.5 PUMP SPECIFIC SPEED -Raising the flow coefficient CQ = Q/(ωD ) to the power 1, the head coefficient CH = 2 -gH/(ω D ) to the power 3, and forming the ratio of the former to that of the latter, D will be eliminated Calling this ratio as Ns produces the expression ω Q N s = 3/4 ( gH ) (4.43) If the dimensions of Ns are substituted, it will be found dimensionless and because it is dimensionless, it can be used as a general characterization for a whole variety of pumps without reference to their sizes Thus, a certain range of the value of Ns would be a particular type of pump such as axial (no size considered), and another range would be another particular type of pump such as radial (no size considered) Ns is called specific speed By characterizing all the pumps generally like this, Ns is of great applicability in selecting the proper type of pump, whether radial or axial or any other type For example, refer to Figure 4.9 The radial-vane pumps are in the range of Ns = 9.6 to 19.2; the Francis-vane pumps are in the range of 28.9 to 76.9; and so on Therefore, if Q, ω, and H are known, Ns can be computed using Equation (4.43); thus, depending upon the value obtained, the type of pump can be specified Just how is the chart of specific speeds obtained? Remember that one of the characteristics curves of a pump is the plot of the efficiency Referring to Figure 4.8, along any curve characterized by a parameter such as rpm, there are an infinite number of efficiency values Of these infinite number of values, there is only one maximum As mentioned previously, this maximum is the best efficiency point If values of ω, Q, and H are taken from the characteristics curves at the best operating efficiencies and substituted into Equation (4.43), values of specific speeds are obtained at these efficiencies For example, from Figure 4.8 at a Q of 0.16 m /s, the best efficiency is approximately 66% corresponding to a total developed head © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 230 Friday, June 14, 2002 4:25 PM Efficiency (%) 100 90 over 0.6333 3 m 80 0.633 m3 0.6333 m 0.03173 m3 0.1900 m 0.0127 m 70 0.0063 m3 60 50 40 30 20 10 9.6 11.5 15.4 19.2 26.9 28.9 57.2 76.9 96.2 113.4 153.9192.3 288.9 384.6 Specific speed, metric units Impeller shrouds Impeller shrouds Impeller Hub Hub Hub Hub hub Vanes Vanes Vanes Vanes Vanes Axis of Radial-vane area Funnels-vane area Mixed-flow area Axial-flow area rotation propellers FIGURE 4.9 Specific speeds of various types of centrifugal pumps of about 13 meters and an rpm of 990 These values substituted into Equation (4.43), after converting the rpm of 990 rpm to radians per second, produces an Ns of 1.73 A number of calculations similar to this one need to be done on other characteristics curves in order to produce Figure 4.9 In other words, this figure has been obtained under conditions of best operating efficiencies Therefore, specifying pumps using specific speeds as the criterion and using figures such as Figure 4.9 ensures that the pump selected operates at the best operating efficiency From this discussion, it can be gleaned that specific speed could have gotten its name from the fact that its value is specific to the operating conditions at the best operating efficiency Example 4.6 A designer wanted to recommend the use of an axial-flow pump to move wastewater to an elevation of 30 m above a sump Overall friction losses of the system and the velocity at the discharge side are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m Is the designer recommending the right pump? Design the pump yourself Solution: ω Q N s = 3/4 ( gH ) 2 P P V2 V1 – h lp + h p = TDH = – + - – - + h fs + h fd + h st γ γ 2g 2g © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 231 Friday, June 14, 2002 4:25 PM Take the sump pool level as point and the sewage discharge level as point 2 V /2g = 0, because the pool velocity is zero Points and are both exposed to the atmosphere 2 V2 1.30 - = - = 0.086 m 2g ( 9.81 ) P P TDH =  – 1 = + 0.086 – + 20 + 30 = 50.086 m γ γ ω = 1,200 ( π )/60 = 125.67 radians/s πD π ( 0.225 ) A d = cross-section of discharge pipe = - = - = 0.040 m 4 2 Therefore, Q = ( 1.3 ) ( 0.040 ) = 0.052 m /s 125.67 0.052 N s = = 0.27 3/4 [ ( 9.81 ) ( 50.086 ) ] This falls outside the range of specific speeds in Figure 4.9; however, the pump should not be an axial flow pump as recommended by the designer Ans From the figure, for a Q of 0.052 m /s and an Ns of 0.27, the pump would have to be of radial-vane type Ans 4.6 NET POSITIVE SUCTION HEAD AND DEEP-WELL PUMPS In order for a fluid to enter the pump, it must have sufficient energy to force itself toward the inlet This means that a positive head (not negative head) must exist at the pump inlet This head that must exist for pumping to be possible is termed the net positive suction head (NPSH) It is an absolute, not gage, positive head acting on the fluid Refer to the portion of Figure 4.6 where the source tank fluid level is below the center line of the impeller in either the system connected in parallel or in the system connected in series At the surface of the wet well (point 1), the pressure acting on the liquid is equal to the atmospheric pressure Patm minus the vapor pressure of the liquid Pv This pressure is, thus, the atmospheric pressure corrected for the vapor pressure and is the pressure pushing on the liquid surface Imagine the suction pipe devoid of liquid; if this is the case, then this pressure will push the fluid up the suction pipe This is actually what happens as soon as the impeller starts moving and pulling the liquid up As soon as a space is evacuated by the impeller in the suction pipe, liquid rushes up to fill the void; this is not possible, however, without a positive NPSH to push the liquid Note that before the impeller can its job, the fluid must, first, reach it Thus, the need for a driving force at the inlet side The pushing pressure converts to available head or available energy at the suction side of the pump system The surface of the well is below the pump, so this available energy must be subtracted by hᐉ The other substractions are the friction losses hfs © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 232 Friday, June 14, 2002 4:25 PM For the source tank fluid level above the center line of the pump impeller, hs will be added increasing the available energy The losses will, again, be subtracted In symbols, P atm – P v NPSH = – h ᐉ ( or + h s ) – h fs γ (4.44) It is instructive to derive Equation (4.44) by applying the energy equation between the wet well pool surface (point of the lower tank) and the inlet to the pump (a or g) The equation is: 2 V1 V2 P P - + z + – h fs = - + z + 2g γ 2g γ P atm – P v Va P + + – h fs = - + h ᐉ + a γ 2g γ where V1 = velocity at the wet pool level, z1 = elevation of the pool level with reference to a datum (the pool level, itself, in this case), P1 = pressure at pool level, hfs = friction loss from pool level to inlet of pump (the suction side friction loss), Va = velocity at inlet to the pump, za = elevation of the inlet to the pump with reference to the datum (the pool level), and Pa = pressure at the inlet to the pump Pa is the absolute pressure at the pump inlet, i.e., not a gage pressure but an absolute pressure corrected for the vapor pressure of water This type of absolute pressure is not the same as the normal absolute pressure where the prevailing barometric pressure is simply added to the gage reading This is an absolute pressure where the vapor pressure is first subtracted from the gage reading Pgage and then the result added to the prevailing atmospheric pressure In other words, Pa = Pgage − Pv + Patm This produces the true pressure acting on the liquid at the inlet to the pump By also considering the source tank above the center line of the impeller, the final equation after rearranging is: 2 Va P V a P gage – P v + P atm P atm – P v - + a = - + - = – h ᐉ ( or + h s ) – h fs 2g γ 2g γ γ (4.45) Therefore, NPSH is also 2 V a P gage – P v + P atm Va P atm – P v NPSH = - + - = - +  h i +   2g γ 2g  γ (4.46) Note that Pa /γ is equal to Pgage − Pv + Patm /γ = hi + Patm − Pv / γ , where the vapor pressure Pv has been subtracted to obtain the true pressure acting on the fluid as mentioned In simple words, the NPSH is the amount of energy that the fluid possesses at the inlet to the pump It is the inlet dynamic head that pushes the fluid into the pump © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 233 Friday, June 14, 2002 4:25 PM impeller blades Finally, NPSH and cavitation effects must be related If NPSH does not exist at the suction side, cavitation will, obviously, occur The next point to be considered is the influence of the NPSH on deep-well pumps It should be clear that the depth of water that can be pumped is limited by the net positive suction head We have learned, however, that when pumps are connected in series, the heads are added Thus, it is possible to pump groundwater from any depth, if impellers of the pump are laid out in series This is the principle used in the design of deep-well pumps Refer to the deep-well pump of Figure 4.3 This pump is shown to have two stages The water lifted by the first stage is introduced to the second stage And, since the stages are in series, the head developed in the first stage is added to that of the second stage Thus, this pump is capable of pumping water from deeper wells Deep-well pumps can be designed for any number of stages, within practical limits Because of the limitation of the NPSH, these pumps must obviously be lowered toward the bottom at a distance sufficient to have a positive NPSH on the first impeller, with an ample margin of safety Provide a margin of safety in the neighborhood of 90% of the calculated NPSH In other words, if the computed NPSH is in the neighborhood of m, for example, assume it to be 0.9(7) ≈ m Example 4.7 A wastewater is to be pumped to an elevation of 30 m above a sump Overall friction losses of the system and the velocity at the discharge side are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 mm and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m What is the NPSH? Solution: The formula to be used is Equation 4.44 P atm – P v NPSH = – h ᐉ – h fs γ Not all of these variables are given; therefore, some assumptions are necessary In an actual design, this is what is actually done; the resulting design, of course, must be shown to work Assume standard atmosphere and 20°C P atm = 101,325 N/m P v = 2340 N/m γ = 997 ( 9.81 ) N/m h ᐉ = m h fs = 1.03 m 101,325 – 2340 Therefore, NPSH = - – – 1.03 = 7.09 m of water Ans 997 ( 9.81 ) 4.7 PUMPING STATION HEAD ANALYSIS The pumping station (containing the pumps and station appurtenances) and the system piping constitute the pumping system In this system, there are two types of characteristics: the pump characteristics and the system characteristic The term system characteristic refers to the characteristic of the system comprising everything that contains the flow except the pump casing and the impeller inside it © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 234 Friday, June 14, 2002 4:25 PM Specifically, system characteristic is the relation of discharge Q and the associated head requirements of this system which, again, does not include the pump arrangement The pump arrangement may be called the pump assembly In the design of a pumping station, both the pump characteristics and the system characteristic must be considered simultaneously For convenience, reproduce the formulas for TDH as follows: TDH = TDH0sd = h st + h fs + h fd (a) TDH = TDH0rm = h st + h fr + h fm (b) P B – P atm V B TDH = TDHfullsd = + - + z + h fs + h fd γ 2g (c) P B – P atm V B TDH = TDHfullrm = + - + z + h fr + h fm γ 2g 2 P Vo P Vi TDH = TDHmano =  o + -  –  i + -   γ 2g  γ 2g TDHabso = h abso + h vo – ( h absi + h vi ) TDH = TDHdh = odh – idh (d) (e) (f) (g) TDH is the “total developed head” developed inside the pump casing, that is, developed by the pump assembly This TDH is equal to any of the right-hand-side expressions of the above equations If the TDH on the left refers to the pump assembly, then the right-hand-side expressions must refer to the system piping By assuming different values of discharge Q, corresponding values of the right-handside expressions can be calculated These values are head loss equivalents corresponding to the Q assumed This is the relationship of the various Qs and head losses in the system characteristic mentioned above As can be seen, these head losses are head loss requirements for the associated Q It is head loss requirements that the TDH of the pump assembly must satisfy Call head loss requirements TDHR TDHR, therefore, requires the TDH of the pump It should be obvious that, if the TDH of the pump assembly is less than the TDHR of the system piping, no fluid will flow To ensure that the proper size of pumps are chosen for a given desired pumping rate, the TDH of the pumps must be equal to the TDHR of the system piping This is easily done by plotting the pump head-discharge-characteristic curve and the system-characteristic curve on the same graph The point of intersection of the two curves is the desired operating point The principle of series or parallel connections of pumps must be used to arrive at the proper pump combination to suit the desired system characteristic requirement The specific speed should be checked to ensure that the pump assembly selected operates at the best operating efficiency The system piping is composed of the suction piping and the discharge piping system Both the suction and the discharge piping systems would include the piping © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 235 Friday, June 14, 2002 4:25 PM 50 40 Pump System Head (m) head capacity curve 30 P2 and mPI 20 added horizontally (PI) Pump (mPI) 10 P2 PI Station loss 0.1 0.2 0.3 0.4 0.5 Discharge (m 3/a) FIGURE 4.10 Use of pump and system head-discharge characteristics curves for sizing pumping stations (From Peavy, H S., D R Rowe, and G Tchobanoglous (1985) Environmental Engineering McGraw-Hill, New York, 395 With permission.) inside the pumping station, itself For the purpose of system head calculations, it is convenient to disregard the head losses of the pumping station piping and the suction piping The disregarded pumping station and suction piping losses are designated as station losses and applied as corrections to the pump head-discharge curve supplied by the manufacturer This correction produces the effective pump head-discharge curve The discharge piping losses is also corrected by those portions of this loss assigned to the pumping station losses An illustration of sizing pumping stations is shown in Figure 4.10 and in the next example Example 4.8 Calculations for the system characteristic curve yield the following results: Q (m /s) TDHR (m) Q (m /s) TDHR (m) Q (m /s) TDHR (m) 0.0 0.3 10.00 17.59 0.1 0.4 10.84 23.48 0.2 0.5 13.37 31.06 The station losses are as follows: Pump No 3 Q (m /s) hf (m) Q (m /s) hf (m) Q (m /s) hf (m) 0.0 0.00 0.1 0.14 0.2 0.56 © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 236 Friday, June 14, 2002 4:25 PM Pump No 3 Q (m /s) hf (m) Q (m /s) hf (m) Q (m /s) hf (m) 0.0 0.3 0.00 0.58 0.1 0.4 0.06 1.03 0.2 0.26 If two pumps with head-discharge characteristics plotted in Figure 4.10 (dashed lines) are to be used, (a) determine the pumping system discharges when each pump is operated separately and, when both pumps are operated in parallel (b), determine at what head will both pumps operated in series deliver a discharge of 0.2 m /s Solution: (a) The system head-discharge or head-capacity curve is plotted as shown in the figure The pump head-discharge curves supplied by the manufacturer (dashed lines) are modified by the head losses as given above The resulting effective head-discharge curves are drawn in solid lines designated as mP1 and mP2 for pumps and 2, respectively The intersection of the effective head-discharge curve and the system curve, when only pump no is operating, is 0.2 m /s This is the pumping system discharge Ans When only pump no is operating, the system discharge is 0.31 m /s Ans When both are operated in parallel, the effective characteristic curve for pump no is shifted horizontally to the right until the top end of the curve coincides with a portion of the effective curve of pump no 2, as shown This has the effect of adding the discharges for parallel operation As indicated, when both are operated in parallel, the system discharge is 0.404 m /s Ans (b) For the operation in series, the TDH for pump no for a system discharge of 0.2 m /s is 13 m That of pump no is 32 m Therefore, the system TDH is 32 + 13 = 45 m Ans GLOSSARY Axial-flow pumps—Pumps that transmit the fluid pumped in the axial direction Best operating efficiency—Value of the efficiency that corresponds to the best operating performance of the pump Brake or shaft power—The power of the motor or prime mover driving the pump Brake efficiency—Ratio of the power given to the fluid to the brake input power (brake power) to the pump Cavitation—A state of flow where the pressure in the liquid becomes equal to its vapor pressure Centrifugal pump—A pump that conveys fluid through the momentum created by a rotating impeller Discharge—In a pumping system, the arrangement of elements after the pumping station Discharge velocity head—The velocity head at the discharge of a pumping system © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 237 Friday, June 14, 2002 4:25 PM Displacement pumps—Pumps that literally pushes the fluid in order to move it Dynamically similar pumps—Pumps with head coefficients that are equal Fittings losses—Head losses in valves and fittings Flow coefficient CQ—The group Q/(ω D ) Friction head loss—A head loss due to loss of internal energy Gear pump—A pump that basically operate like a lobe pump, except that instead of lobes, gear teeth are used to move the fluid Geometrically similar pumps—Pumps with corresponding parts that are proportional 2D Head coefficient CH—The group Hg/(ω D ) Homologous pumps—Pumps that are similar Similarities are established dynamically, kinematically, or geometrically Inlet dynamic head—The sum of the inlet velocity head and inlet manometric head of a pump Inlet manometric head—The manometric level at the inlet to a pump Kinematically similar pumps—Pumps whose flow coefficients are equal Lobe pump—A positive-displacement pump whose impellers are shaped like lobes Manifold pipe—A pipe with two or more pipes connected to it Manometric level—The height of liquid corresponding to the gage pressure Mixed-flow pump—Pump with an impeller that is designed to provide a combination of forward and radial flow Net positive suction head (NSPH)—The amount of energy possessed by a fluid at the inlet to a pump Non-pivot parameter—The counterpart of pivot parameter Outlet dynamic head—The sum of the outlet velocity head and outlet manometric head of a pump Outlet manometric head—The manometric level at the outlet of a pump Parallel connection—Mode of connection of more than one pump where the discharges of all the pumps are combined into one Positive-displacement pump—A pump that conveys fluid by directly moving it using a suitable mechanism such as a piston, plunger, or screw Power coefficient CP —The group P /ρω D Propeller pumps—The same as axial-flow pumps Pump assembly—The pump arrangement in a pumping station Pump characteristics—Set of curves that depicts the performance of a given particular pump Pump loss—Head losses incurred inside the pump casing Pumping—A unit operation used to move fluid from one point to another Pumping station—A location where one or more pumps are operated to convey fluids Pumping system—The pumping station and the piping system constitute the pumping system Radial-flow pump—Pump with an impeller that directly throws the flow radially into the side of the chamber circumscribing it Scaling laws—Mathematical equations that establish the similarity of homologous pumps © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 238 Friday, June 14, 2002 4:25 PM Series connection—A mode of connecting more than one pump where the discharge of the pump ahead is introduced to the inlet of the pump following Similar or homologous pumps—Pumps where the head, flow, and pressure coefficients are equal Similarity, affinity, or scaling laws—The equations that state that the head, flow, and power coefficients of a series of pumps are equal Specific speed—A ratio obtained by manipulating the ratio of the flow coefficient to the head coefficient of a pump Values obtained are values applying at the best operating efficiency Static discharge head—The vertical distance from the pump centerline to the elevation of the discharge liquid level Static suction head—The vertical distance from the elevation of the inflow liquid level above the pump centerline to the centerline of the pump Static suction lift—The vertical distance from the elevation of the inflow liquid level below the pump centerline to the centerline of the pump Suction—In a pumping system, the system of elements before the pumping station Suction velocity head—The velocity head at the suction side of a pumping system System characteristic—In a pumping system, the relationship of discharge and the associated head requirement that excludes the pump assembly Total dynamic head or total developed head—The head given to the pump minus pump losses Total developed head requirement—The equivalent head loss corresponding to a given discharge Total static head—The vertical distance between the elevation of the inflow liquid level and the discharge liquid level Transition losses—Head losses in expansions, contractions, bends, and the like Turbomachine—Fluid machine that turns or tends to turn about an axis Vane pump—A pump in which a vane pushes the water forward as it is being trapped between the vane and the side of the casing Volute—Casing of a centrifugal pump that is shaped into a spiral SYMBOLS CH CQ CP D g hbrake hf hfd hfm Head coefficient Flow coefficient Power coefficient Diameter of centrifugal pump or length of stroke of reciprocating pump Earth’s gravitational acceleration Head equivalent to brake power input to pump from a prime mover Friction head loss Discharge side friction losses Minor head losses © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 239 Friday, June 14, 2002 4:25 PM hfr hfs hi hᐉ hlp ho hp hq hs hst hvi hvo idh H Ns NPSH odh P Patm Pgage Pv ∆P P Q TDH TDHR V z γ η ρ ω µ Head losses due to straight runs of pipes Suction side friction losses Inlet manometric head Suction lift Pump loss Outlet manometric head Head given to pump Head equivalent to heat added to system Suction head Total static head Inlet velocity head Outlet velocity head Inlet dynamic head Total dynamic or developed head, TDH Specific speed Net positive suction head Outlet dynamic head Pressure Barometric pressure Gage reading of pressure Vapor pressure of water Developed pressure, equivalent to total developed head Power to fluid Rate of discharge Total dynamic or developed head Total developed head requirement Velocity Elevation of fluid from a reference datum Specific weight of water pump efficiency Density of water Speed of pump in radians per second absolute or dynamic viscosity PROBLEMS 4.1 4.2 4.3 Water at a temperature of 22°C is to be conveyed from a reservoir with a water surface elevation of 70 m to another reservoir 300 m away with a water surface elevation of 20 m Determine the diameter of a steel pipe if the flow is 2.5 m /s Assume a square-edged inlet and outlet as well as two open gate valves in the system For the pump represented in Figure 4.8, determine the discharge when the pump is operating at a head of 20 m at a speed of 1,100 rpm Calculate the efficiency and power for the pump in Problem 4.2 © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 240 Friday, June 14, 2002 4:25 PM 240 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 Physical–Chemical Treatment of Water and Wastewater If the pump in Problem 4.2 is operated at 1,170 rpm, calculate the resulting H, Q, Pbrake , and η If a homologous 30-cm pump is to be used in Problem 4.2, calculate the resulting H, Q, Pbrake , and η for the same rpm The outlet manometric head at the discharge of a pump is equal to the equivalent of 50 m of water If the discharge velocity is 2.0 m/s, what is the outlet dynamic head? You are required to recommend the type of pump to be used to convey wastewater to an elevation of m above a sump Friction losses and the velocity at the sewage discharge level are estimated to be m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 mm and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m What type of pump would you recommend? In Problem 4.7, if the temperature is 20°C, has cavitation occurred? Compute the inlet and outlet manometric heads in Problem 4.7 In Problem 4.7, what are the inlet and outlet dynamic heads? From the values of idh and odh, calculate TDH In Problem 4.7, what is the NPSH? In Example 4.8, calculate the percent errors in the answers if the characteristic curves of the pumps are not corrected for the station losses What is −hlp + hp equal to? Explain why this expression is given this name What is the name given to the pressure that is equivalent to the pressure head? What are inlet dynamic head and outlet dynamic head? It is desired to pump a wastewater to an elevation of 30 m above a sump Friction losses and velocity at the discharge side of the pump system are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 mm and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m If the temperature is 10°C, has cavitation occurred? What are the inlet and outlet manometric heads in Problem 4.16? What are the inlet and outlet total dynamic heads in Problem 4.16? From the values of the idh and odh, calculate TDH In relation to hlp, discuss the relationship of hp and hbrake Show all the steps in the derivation of Equation (4.27) It is desired to pump a wastewater to an elevation of 30 m above a sump Friction losses and velocity at the discharge side of the pump system are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm The diameter of the suction and discharge lines are 250 mm and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is m If the temperature is 10°C and the inlet manometric head is −3.09 m, what are the suction friction losses? In Problem 4.21, what is the head given to the pump? © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 241 Friday, June 14, 2002 4:25 PM Pumping 241 4.23 Pump characteristics curves are developed in accordance with the setup of Figure 4.7 The discharge flow is 0.15 m /s and the outlet diameter of the discharge pipe is 375 mm The motor driving the pump is 50 hp Calculate the gage pressure at the outlet of the pump 4.24 Pump characteristics curves are developed in accordance with the setup of Figure 4.7 The pressure at the outlet of the pump is found to be 196 kN/m gage The outlet diameter of the discharge pipe is 375 mm The motor driving the pump is 50 hp Calculate the rate of discharge 4.25 Pump characteristics curves are developed in accordance with the setup of Figure 4.7 The pressure at the outlet of the pump is found to be 196 kN/m gage The outlet diameter of the discharge pipe is 375 mm If the rate of discharge is 0.15 m /s, calculate the input brake power to the pump 4.26 In Problem 4.25, if the brake efficiency is 65%, calculate Po, hbrake, and Vo 4.27 If the pump in Example 4.4 has a power input of 30 kW, determine the rpm 4.28 In Problem 4.27, calculate the resulting H 4.29 In Problem 4.27, calculate the resulting Q and η 4.30 If a homologous 40-cm pump is to be used for the problem in Example 4.5, calculate the resulting H, Q, Pbrake , and η for the same rpm 4.31 A designer wanted to recommend the use of an axial-flow pump to move wastewater to an elevation of 50 m above a sump Friction losses and velocity at the discharge side of the pumping system are estimated to be 20 m and 1.30 m/s, respectively The operating drive is to be 1,200 rpm Suction friction losses are 1.03 m; the diameter of the suction and discharge lines are 250 mm and 225 mm, respectively The vertical distance from the sump pool level to the pump centerline is 15 m Is the designer recommending the right pump? What is the net positive suction head? Is the pumping possible? BIBLIOGRAPHY Bosserman, B and P Behnke (1998) Selection criteria for wastewater pumps Water/Eng Manage 145, 10 Foster, R S (1998) Surge protection design for the city and county of San Francisco water transmission system Pipelines in the Constructed Environment, Proc 1998 Pipeline Div Conf., Aug 23–27, San Diego, CA, 103–112, ASCE, Reston, VA Foster, R S (1998) Analysis of surge pressures in the inland feeder and eastside pipeline Proc Pipelines in the Constructed Environment, Proc 1998 Pipeline Div Conf., Aug 23–27, San Diego, CA, 88–96, ASCE, Reston, VA Franzini, J B and E J Finnemore (1997) Fluid Mechanics McGraw-Hill, New York Granet, I (1996) Fluid Mechanics Prentice Hall, Englewood Cliffs, NJ Hammer, M J (1986) Water and Wastewater Technology John Wiley & Sons, New York Kotov, A I (1998) Water treatment system is one of the most important elements of the ecological safety of the plant Tyazheloe Mashinostroenie, 7, 58–60 Nahm, E S and K B Woo (1998) Prediction of the amount of water supplied in wide-area waterworks Proc 1998 24th Annu Conf IEEE Industrial Electron Soc., IECON, Part 1, Aug 31–Sept 4, Aachen, Germany, 1, 265–268 IEEE Comp Soc., Los Alamitos, CA © 2003 by A P Sincero and G A Sincero 249_frame_CH-04 Page 242 Friday, June 14, 2002 4:25 PM 242 Physical–Chemical Treatment of Water and Wastewater Plakhtin, V D (1998) Hydropneumatic system for balancing spindles of the breakdown at Mill 560 Stal, 3, 45–47 Peavy, H S., D R Rowe, and G Tchobanoglous (1985) Environmental Engineering McGrawHill, New York Qasim, S R (1985) Wastewater Treatment Plants Planning, Design, and Operation Holt, Rinehart & Winston, New York Shafai-Bajestan, M., A Behzadi-Poor, S R Abt, (1998) Control of sediment deposition at the Amir-Kabir pump station using a physical hydraulic model Int Water Resour Eng Conf.—Proc 1998 Int Water Resour Eng Conf., Part 2, Aug 3–7, Memphis, TN, 2, 1553–1558, ASCE, Reston, VA Shames, I (1992) Mechanics of Fluids McGraw-Hill, New York Shi, W (1998) Design of axial flow pump hydraulic Model ZM931 on high specific speed Nongye Jixie Xuebao/Trans Chinese Soc Agricultural Machinery, 29, 2, 48–52 Sincero, A P and G A Sincero (1996) Environmental Engineering: A Design Approach Prentice Hall, Upper Saddle River, NJ Smolyanskij, B G., O V Bakulin, and O E Volkov (1998) Advanced pump equipment for the acceptance and delivery of petroleum products at warehouses Khimicheskoe I Neftyanoe Mashinostroenie, 6, 38–40 Spencer, R C., L G Grainger, V G Peacock, and J Blois (1998) Building a 5000 hp, VFD Controlled Pump Station in 105 Days “Fact or Fantasy.” Proc 1998 International Pipeline Conference, IPC, Part 2, June 7–11, Calgary, Canada, 2, 1111–1117 ASME, Fairfield, NJ Vlasov, V S (1998) High pressure pump stations and their application fields Tyazheloe Mashinostroenie, 7, July, 53–55 Wang, X T et al (1998) Modeling and remediation of ground water contamination at the Engelse Werk Wellfield Ground Water Monitoring Remediation, 18, 3, 114–124 Zheng, Y., et al (1998) Hydraulic design and analysis for a water supply system modification Proc 1998 Int Water Resour Eng Conf., Part 2, Aug 3–7, Memphis, TN, 2, 1673–1678 ASCE, Reston, VA © 2003 by A P Sincero and G A Sincero ... the pump At 20°C, Pv (vapor pressure of water) = 2.34 kN/m = 0.239 m of water Assume standard atmosphere of atm = 10.34 m of water Therefore, theoretical limit of pump cavitation = − (10.34 − 0.239)... sectional area of pipe π ( 0.375 ) /4 Assume temperature of water = 25°C; therefore, density of water = 997 kg/m 196 ( 1000 ) 1.36 TDH = - + - = 20.13 m of water 997 ( 9.81... Elevation of fluid from a reference datum Specific weight of water pump efficiency Density of water Speed of pump in radians per second absolute or dynamic viscosity PROBLEMS 4.1 4.2 4.3 Water at