In Prob. P11.31, the pump BEP fl ow rate is 2000 gal/min, the impeller diameter is 16

8 A rectangular channel 4 m wide is blocked by a broad-crested weir 2 m high, as in Fig. P10.128. The channel is horizontal for 200 m upstream and then slopes at 0.78 as shown. The fl ow rate is 12 m3 /s, and n 5 0.03. Compute the water depth y at 300 m upstream from gradually varied theory. y? y(x) Slope 0.7 12 m3/s 200 m 100 m

What would be the technical classifi cation of the following turbomachines: (a) a household fan, (b) a windmill, (c) an aircraft propeller, (d ) a fuel pump in a car, (e) an eductor, (f ) a fl uid-coupling transmission, and (g) a power plant steam turbine?

A PDP can deliver almost any fl uid, but there is always a limiting very high viscosity for which performance will deteriorate. Can you explain the probable reason?

Figure P11.4 shows the impeller on a common device which, when operating, turns at up to 300,000 r/min. Can you guess what it is and offer a description? P11.4 [Image provided by Sigma-Aldrich Corporation.]

What type of pump is shown in Fig. P11.5? How does it operate?

Figure P11.6 shows two points a half-period apart in the operation of a pump. What type of pump is this [13]? How does it work? Sketch your best guess of fl ow rate versus time for a few cycles.

A piston PDP has a 5-in diameter and a 2-in stroke and operates at 750 r/min with 92 percent volumetric effi ciency. (a) What is its delivery, in gal/min? (b) If the pump delivers SAE 10W oil at 208C against a head of 50 ft, what horsepower is required when the overall effi ciency is 84 percent?

A Bell and Gossett pump at best effi ciency, running at 1750 r/min and a brake horsepower of 32.4, delivers 1050 gal/min against a head of 105 ft. (a) What is its effi ciency? (b) What type of pump is this?

Figure P11.9 shows the measured performance of the Vickers model PVQ40 piston pump when delivering SAE 10W oil at 1808F ( < 910 kg/m3 ). Make some general observations about these data vis--vis Fig. 11.2 and your intuition about the behavior of piston pumps.

Suppose that the pump of Fig. P11.9 is run at 1100 r/min against a pressure rise of 210 bar. (a) Using the measured displacement, estimate the theoretical delivery in gal/min. From the chart, estimate (b) the actual delivery and (c) the overall effi ciency.

A pump delivers 1500 L/min of water at 208C against a pressure rise of 270 kPa. Kinetic and potential energy changes are negligible. If the driving motor supplies 9 kW, what is the overall effi ciency?

2 In a test of the centrifugal pump shown in Fig. P11.12, the following data are taken: p1 5 100 mmHg (vacuum) and p2 5 500 mmHg (gage). The pipe diameters are D1 5 12 cm and D2 5 5 cm. The fl ow rate is 180 gal/min of light oil (SG 5 0.91). Estimate (a) the head developed, in meters, and (b) the input power required at 75 percent effi ciency.p2 5500 kPa, z2 5 4 m, and V2 5 3 m/s. How much power is required if the motor effi ciency is 75 percent? P11.12 (2) 65 cm (

A 3.5 hp pump delivers 1140 lbf of ethylene glycol at 208C in 12 seconds, against a head of 17 ft. Calculate the effi - ciency of the pump.

4 A pump delivers gasoline at 208C and 12 m3 /h. At the inlet p1 5 100 kPa, z1 5 1 m, and V1 5 2 m/s. At the exit p2 5 500 kPa, z2 5 4 m, and V2 5 3 m/s. How much power is required if the motor effi ciency is 75 percent? P11

A lawn sprinkler can be used as a simple turbine. As shown in Fig. P11.15, fl ow enters normal to the paper in the center and splits evenly into Q/2 and Vrel leaving each nozzle. The arms rotate at angular velocity and do work on a shaft. Draw the velocity diagram for this turbine. Neglecting friction, fi nd an expression for the power delivered to the shaft. Find the rotation rate for which the power is a maximum. P11.15 R Q R Q 2 , Vrel Q 2 , Vrel

The centrifugal pump in Fig. P11.16 has r1 5 15 cm, r2 5 25 cm, b1 5 b2 5 6 cm, and rotates counterclockwise at 600 r/min. A sample blade is shown. Assume 1 5 908. Estimate the theoretical fl ow rate and head produced, for water at 208C, and comment. P11.16 Impeller 40 30 150

7 A centrifugal pump has d1 5 7 in, d2 5 13 in, b1 5 4 in, b2 5 3 in, 1 5 258, and 2 5 408 and rotates at 1160 r/min. If the fl uid is gasoline at 208C and the fl ow enters the blades radially, estimate the theoretical (a) fl ow rate in gal/min, (b) horsepower, and (c) head in ft.

A jet of velocity V strikes a vane that moves to the right at speed Vc, as in Fig. P11.18. The vane has a turning angle . Derive an expression for the power delivered to the vane by the jet. For what vane speed is the power maximum?

A centrifugal pump has r2 5 9 in, b2 5 2 in, and 2 5 358 and rotates at 1060 r/min. If it generates a head of 180 ft, determine the theoretical (a) fl ow rate in gal/min and (b) horsepower. Assume near-radial entry fl ow.

Suppose that Prob. P11.19 is reversed into a statement of the theoretical power Pw < 153 hp. Can you then compute the theoretical (a) fl ow rate and (b) head? Explain and resolve the diffi culty that arises.

The centrifugal pump of Fig. P11.21 develops a fl ow rate of 4200 gal/min of gasoline at 208C with near-radial absolute infl ow. Estimate the theoretical (a) horsepower, (b) head rise, and (c) appropriate blade angle at the inner radius. 30 1750 r/min 2 in 4 in 3

A 37-cm-diameter centrifugal pump, running at 2140 r/min with water at 208C, produces the following performance data: Q, m3 /s 0.0 0.05 0.10 0.15 0.20 0.25 0.30 H, m 105 104 102 100 95 85 67 P, kW 100 115 135 171 202 228 249 (a) Determine the best effi ciency point. (b) Plot CH versus CQ. (c) If we desire to use this same pump family to deliver 7000 gal/min of kerosene at 208C at an input power of 400 kW, what pump speed (in r/min) and impeller size (in cm) are needed? What head will be developed?

When pumping water, (a) at what speed should the 11-in Bell and Gossett centrifugal pump of Prob. P11.8 be run, at best effi ciency, to deliver 800 gal/min? Estimate the resulting (b) head, and (c) brake horsepower

4 Figure P11.24 shows performance data for the Taco, Inc., model 4013 pump. Compute the ratios of measured shutoff head to the ideal value U2 /g for all seven impeller sizes. Determine the average and standard deviation of this ratio and compare it to the average for the six impellers in Fig. 11.7

At what speed in r/min should the 35-in-diameter pump of Fig. 11.7b be run to produce a head of 400 ft at a discharge of 20,000 gal/min? What brake horsepower will be required? Hint: Fit H(Q) to a formula

Would the smallest, or the largest, of the seven Taco, Inc. pumps in Fig. P11.24 be better (a) for producing, near best effi ciency, a water fl ow rate of 600 gal/min and a head of 95 ft? (b) At what speed, in r/min, should this pump be run? (c) What input power is required?

The 11-in Bell and Gossett pump of Prob. P11.8 is to be scaled up to provide, at best effi ciency, a head of 250 ft and a fl ow rate of 3000 gal/min. Find the appropriate (a) impeller diameter; (b) speed in r/min; and (c) horsepower required.

Tests by the Byron Jackson Co. of a 14.62-in-diameter centrifugal water pump at 2134 r/min yield the following data: Q, ft3 /s 0 2 4 6 8 10 H, ft 340 340 340 330 300 220 bhp 135 160 205 255 330 330 What is the BEP? What is the specifi c speed? Estimate the maximum discharge possible.

Tests by the Byron Jackson Co. of a 14.62-in-diameter centrifugal water pump at 2134 r/min yield the following data: Q, ft3 /s 0 2 4 6 8 10 H, ft 340 340 340 330 300 220 bhp 135 160 205 255 330 330 What is the BEP? What is the specifi c speed? Estimate the maximum discharge possible.

A pump, geometrically similar to the 12.95-in model in Fig. P11.24, has a diameter of 24 in and is to develop 30 hp at BEP when pumping gasoline (not water). Determine (a) the appropriate speed, in r/min; (b) the BEP head, in ft; and (c) the BEP fl ow rate, in gal/min.

A centrifugal pump with backward-curved blades has the following measured performance when tested with water at 208C: Q, gal/min 0 400 800 1200 1600 2000 2400 H, ft 123 115 108 101 93 81 62 P, hp 30 36 40 44 47 48 46 (a) Estimate the best effi ciency point and the maximum effi ciency. (b) Estimate the most effi cient fl ow rate, and the resulting head and brake horsepower, if the diameter is doubled and the rotation speed increased by 50 percent

The data of Prob. P11.31 correspond to a pump speed of 1200 r/min. (Were you able to solve Prob. P11.31 without this knowledge?) (a) Estimate the diameter of the impeller. [Hint: See Prob. P11.24 for a clue.] (b) Using your estimate from part (a), calculate the BEP parameters C* Q, C* H, and C* P and compare with Eqs. (11.27). (c) For what speed of this pump would the BEP head be 280 ft?

In Prob. P11.31, the pump BEP fl ow rate is 2000 gal/min, the impeller diameter is 16 in, and the speed is 1200 r/min. Scale this pump with the similarity rules to fi nd (a) the diameter and (b) the speed that will deliver a BEP water fl ow rate of 4000 gal/min and a head of 180 ft. (c) What brake horsepower will be required for this new condition?

You are asked to consider a pump geometrically similar to the 9-in-diameter Taco pump of Fig. P11.34 to deliver 1200 gal/min at 1500 r/min. Determine the appropriate (a) impeller diameter, (b) BEP horsepower, (c) shutoff head, and (d ) maximum effi ciency. The fl uid is kerosene, not water.

An 18-in-diameter centrifugal pump, running at 880 r/min with water at 208C, generates the following performance data: Q, gal/min 0.0 2000 4000 6000 8000 10,000 H, ft 92 89 84 78 68 50 P, hp 100 112 130 143 156 163 Determine (a) the BEP, (b) the maximum effi ciency, and (c) the specifi c speed. (d ) Plot the required input power versus the fl ow rate.

The pump of Prob. P11.35 has a maximum effi ciency of 88 percent at 8000 gal/min. (a) Can we use this pump, at the same diameter but a different speed, to generate a BEP head of 150 ft and a BEP fl ow rate of 10,000 gal/min? (b) If not, what diameter is appropriate?

Consider the two pumps of Problems P11.28 and P11.35. If the diameters are not changed, which is better for delivering water at 3000 gal/min and a head of 400 ft? What is the appropriate rotation speed for the better pump?

A 6.85-in pump, running at 3500 r/min, has the following measured performance for water at 208C: Q, gal/min 50 100 150 200 250 300 350 400 450 H, ft 201 200 198 194 189 181 169 156 139 , % 29 50 64 72 77 80 81 79 74 (a) Estimate the horsepower at BEP. If this pump is rescaled in water to provide 20 bhp at 3000 r/min, determine the appropriate (b) impeller diameter, (c) fl ow rate, and (d ) effi - ciency for this new condition

The Allis-Chalmers D30LR centrifugal compressor delivers 33,000 ft3 /min of SO2 with a pressure change from 14.0 to 18.0 lbf/in2 absolute using an 800-hp motor at 3550 r/min. What is the overall effi ciency? What will the fl ow rate and Dp be at 3000 r/min? Estimate the diameter of the impeller

The specifi c speed Ns, as defi ned by Eqs. (11.30), does not contain the impeller diameter. How then should we size the pump for a given Ns? An alternate parameter is the specifi c diameter, Ds, which is a dimensionless combination of Q, gH, and D. (a) If Ds is proportional to D, determine its form. (b) What is the relationship, if any, of Ds to CQ*, CH*, and CP*? (c) Estimate Ds for the two pumps of Figs. 11.8 and 11.13

It is desired to build a centrifugal pump geometrically similar to that of Prob. P11.28 to deliver 6500 gal/min of gasoline at 208C at 1060 r/min. Estimate the resulting (a) impeller diameter, (b) head, (c) brake horsepower, and (d ) maximum effi ciency.

An 8-in model pump delivering 1808F water at 800 gal/min and 2400 r/min begins to cavitate when the inlet pressure and velocity are 12 lbf/in2 absolute and 20 ft/s, respectively. Find the required NPSH of a prototype that is 4 times larger and runs at 1000 r/min.

The 28-in-diameter pump in Fig. 11.7a at 1170 r/min is used to pump water at 208C through a piping system at 14,000 gal/min. (a) Determine the required brake horsepower. The average friction factor is 0.018. (b) If there is 65 ft of 12-in-diameter pipe upstream of the pump, how far below the surface should the pump inlet be placed to avoid cavitation?

The pump of Prob. P11.28 is scaled up to an 18-in diameter, operating in water at best effi ciency at 1760 r/min. The measured NPSH is 16 ft, and the friction loss between the inlet and the pump is 22 ft. Will it be suffi cient to avoid cavitation if the pump inlet is placed 9 ft below the surface of a sea-level reservoir?

Determine the specifi c speeds of the seven Taco, Inc., pump impellers in Fig. P11.24. Are they appropriate for centrifugal designs? Are they approximately equal within experimental uncertainty? If not, why not?

The answer to Prob. P11.40 is that the dimensionless specifi c diameter takes the form Ds 5 D(gH*)1/4/Q*1/2, evaluated at the BEP. Data collected by the author for 30 different pumps indicate, in Fig. P11.46, that Ds correlates well with specifi c speed Ns. Use this fi gure to estimate the appropriate impeller diameter for a pump that delivers 20,000 gal/min of water and a head of 400 ft when running at 1200 r/min. Suggest a curve-fi tted formula to the data. Hint: Use a hyperbolic formula

A pump must be designed to deliver 6 m3 /s of water against a head of 28 m. The specifi ed shaft speed is 20 r/s. What type of pump do you recommend?

Using the data for the pump in Prob. P11.8, (a) determine its type: PDP, centrifugal, mixed-fl ow, or axial-fl ow. (b) Estimate the shutoff head at 1750 r/min. (c) Does this data fi t on Fig. 11.14? (d ) What speed and fl ow rate would result if the head were increased to 160 ft?

Data collected by the author for fl ow coeffi cient at BEP for 30 different pumps are plotted versus specifi c speed in Fig. P11.49. Determine if the values of C* Q for the three pumps in Probs. P11.28, P11.35, and P11.38 also fi t on this correlation. If so, suggest a curve-fi tted formula for the data. 0.400 0.350 0.300 0.250 0.200 0.150 0.100 0.050 0.000 0 500 1000 1500 2000 2500 3000 3500 NS C* Q Data from 30 different pump designs P11.49 Flow coeffi cient at BEP for 30 commercial pumps. P11.50 Data coll

Data collected by the author for power coeffi cient at BEP for 30 different pumps are plotted versus specifi c speed in Fig. P11.50. Determine if the values of C* P for the three pumps in Prob. P11.49 also fi t on this correlation. If so, suggest a curve-fi tted formula for the data. 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 500 1000 1500 2000 2500 3000 3500 Ns C* P Data from 30 different pump designs P11.50 Power coeffi cient at BEP for 30 commercial

An axial-fl ow blower delivers 40 ft3 /s of air that enters at 208C and 1 atm. The fl ow passage has a 10-in outer radius and an 8-in inner radius. Blade angles are 1 5 608 and 2 5 708, and the rotor runs at 1800 r/min. For the fi rst stage compute (a) the head rise and (b) the power required

An axial-fl ow fan operates in sea-level air at 1200 r/min and has a blade-tip diameter of 1 m and a root diameter of 80 cm. The inlet angles are 1 5 558 and 1 5 308, while at the outlet 2 5 608. Estimate the theoretical values of the (a) fl ow rate, (b) horsepower, and (c) outlet angle 2

Figure P11.46 is an example of a centrifugal pump correlation, where Ds is defi ned in the problem. From data in the literature, we can suggest the following correlation for axial-fl ow pumps and fans: Ds < 130 Ns 0.485 for Ns . 8000 where Ns is the dimensional specifi c speed, Eq. (11.30b). Use this correlation to fi nd the appropriate size for a fan that delivers 24,000 ft3 /min of air at sea-level conditions when running at 1620 r/min with a pressure rise of 2 inches of water. Hint: Express the fan head in feet of air, not feet of water

It is desired to pump 50 ft3 /s of water at a speed of 22 r/s, against a head of 80 ft. (a) What type of pump would you recommend? Estimate (b) the required impeller diameter and (c) the brake horsepower

5 Suppose that the axial-fl ow pump of Fig. 11.13, with D 5 18 in, runs at 1800 r/min. (a) Could it effi ciently pump 25,000 gal/min of water? (b) If so, what head would result? (c) If a head of 120 ft is desired, what values of D and n would be better?

Determine if the Bell and Gossett pump of Prob. P11.8 (a) fi ts the three correlations in Figs. P11.46, P11.49, and P11.50. (b) If so, use these correlations to fi nd the fl ow rate and horsepower that would result if the pump is scaled up to D = 24 in but still runs at 1750 r/min.

Performance data for a 21-in-diameter air blower running at 3550 r/min are as follows: Dp, in H2O 29 30 28 21 10 Q, ft3 /min 500 1000 2000 3000 4000 bhp 6 8 12 18 25 Note the fi ctitious expression of pressure rise in terms of water rather than air. What is the specifi c speed? How does the performance compare with Fig. 11.8? What are C* Q, C* H, and C* P?

Aircraft propeller specialists claim that dimensionless propeller data, when plotted as (CT/J2 ) versus (CP/J2 ), form a nearly straight line, y 5 mx 1 b. (a) Test this hypothesis for the data of Fig. 11.16, in the high effi ciency range J 5 V/(nD) equal to 0.6, 0.7, and 0.8. (b) If successful, try this straight line to predict the rotation rate, in r/min, for a propeller with D 5 5 ft, P 5 30 hp, T 5 95 lbf, and V 5 95 mi/h, for sea level standard conditions. Comment

Suppose it is desired to deliver 700 ft3 /min of propane gas (molecular weight 5 44.06) at 1 atm and 208C with a single-stage pressure rise of 8.0 in H2O. Determine the appropriate size and speed for using the pump families of (a) Prob. P11.57 and (b) Fig. 11.13. Which is the better design?

Performance curves for a certain free propeller, comparable to Fig. 11.16, can be plotted as shown in Fig. P11.60, for thrust T versus speed V for constant power P. (a) What is striking, at least to the writer, about these curves? (b) Can you deduce this behavior by rearranging, or replotting, the data of Fig. 11.16? 200 400 600 800 1000 1200 1400 0 0 50 100 Thrust, lbf Speed, mi/h 150 200 250

A mine ventilation fan, running at 295 r/min, delivers 500 m3 /s of sea-level air with a pressure rise of 1100 Pa. Is this fan axial, centrifugal, or mixed? Estimate its diameter in ft. If the fl ow rate is increased 50 percent for the same diameter, by what percentage will the pressure rise change?

The actual mine ventilation fan discussed in Prob. P11.61 had a diameter of 20 ft [Ref. 20, p. 339]. What would be the proper diameter for the pump family of Fig. 11.14 to provide 500 m3 /s at 295 r/min and BEP? What would be the resulting pressure rise in Pa?

3 A good curve-fi t to the head vs. fl ow for the 32-in pump in Fig. 11.7a is H (in ft) < 500 2 (2.9E27) Q2 Q in gal/min Assume the same rotation rate, 1170 r/min, and estimate the fl ow rate this pump will provide to deliver water from a reservoir, through 900 ft of 12-in pipe, to a point 150 ft above the reservoir surface. Assume a friction factor f 5 0.019

A leaf blower is essentially a centrifugal impeller exiting to a tube. Suppose that the tube is smooth PVC pipe, 4 ft long, with a diameter of 2.5 in. The desired exit velocity is 73 mi/h in sea-level standard air. If we use the pump family of Eqs. (11.27) to drive the blower, what approximate (a) diameter and (b) rotation speed are appropriate? (c) Is this a good design?

5 * An 11.5-in-diameter centrifugal pump, running at 1750 r/min, delivers 850 gal/min and a head of 105 ft at best efficiency (82 percent). (a) Can this pump operate efficiently when delivering water at 208C through 200 m of 10- cm-diameter smooth pipe? Neglect minor losses. (b) If your answer to (a) is negative, can the speed n be changed to operate efficiently? (c) If your answer to (b) is also negative, can the impeller diameter be changed to operate efficiently and still run at 1750 rev/min?

It is proposed to run the pump of Prob. P11.35 at 880 r/min to pump water at 208C through the system in Fig. P11.66. The pipe is 20-cm-diameter commercial steel. What fl ow rate in ft3 /min will result? Is this an effi cient application? 4 m Pump 8 m 3 m 20 m 12 m

The pump of Prob. P11.35, running at 880 r/min, is to pump water at 208C through 75 m of horizontal galvanized iron pipe. All other system losses are neglected. Determine the fl ow rate and input power for (a) pipe diameter 5 20 cm and (b) the pipe diameter found to yield maximum pump effi ciency.

A popular small aircraft cruises at 230 km/h at 8500 ft altitude. It weighs 2200 lbf, has a 180-hp engine, a 76- in-diameter propeller, and a drag-area CDA < 5.6 ft2 . The propeller data in Fig. P11.68 is proposed to drive this aircraft. Estimate the required rotation rate, in r/min, and power delivered, in hp. [NOTE: Simply use the coeffi cient pairs. The actual advance ratio is too high.]

The pump of Prob. P11.38, running at 3500 r/min, is used to deliver water at 208C through 600 ft of cast iron pipe to an elevation 100 ft higher. Determine (a) the proper pipe diameter for BEP operation and (b) the fl ow rate that results if the pipe diameter is 3 in

The pump of Prob. P11.28, operating at 2134 r/min, is used with 208C water in the system of Fig. P11.70. (a) If it is operating at BEP, what is the proper elevation z2? (b) If z2 5 225 ft, what is the fl ow rate if d 5 8 in.? z1 = 100 ft Pump

The pump of Prob. P11.38, running at 3500 r/min, delivers water at 208C through 7200 ft of horizontal 5-in-diameter commercial steel pipe. There are a sharp entrance, sharp exit, four 908 elbows, and a gate valve. Estimate (a) the fl ow rate if the valve is wide open and (b) the valve closing percentage that causes the pump to operate at BEP. (c) If the latter condition holds continuously for 1 year, estimate the energy cost at 10 /kWh

Performance data for a small commercial pump are as follows: Q, gal/min 0 10 20 30 40 50 60 70 H, ft 75 75 74 72 68 62 47 24 This pump supplies 208C water to a horizontal 5 8-in-diameter garden hose ( < 0.01 in) that is 50 ft long. Estimate (a) the fl ow rate and (b) the hose diameter that would cause the pump to operate at BEP

3 The Bell and Gossett pump of Prob. P11.8, running under the same conditions, delivers water at 208C through a long, smooth, 8-in-diameter pipe. Neglect minor losses. How long is the pipe?

The 32-in pump in Fig. 11.7a is used at 1170 r/min in a system whose head curve is Hs (ft) 5 100 1 1.5Q2 , with Q in thousands of gallons of water per minute. Find the discharge and brake horsepower required for (a) one pump, (b) two pumps in parallel, and (c) two pumps in series. Which confi guration is best?

Two 35-in pumps from Fig. 11.7b are installed in parallel for the system of Fig. P11.75. Neglect minor losses. For water at 208C, estimate the fl ow rate and power required if (a) both pumps are running and (b) one pump is shut off and isolated. z1 = 200 ft 1 statute mile of cast iron pipe, 24-in diameter Two pumps z2 = 300 ft

Two 32-in pumps from Fig. 11.7a are combined in parallel to deliver water at 608F through 1500 ft of horizontal pipe. If f 5 0.025, what pipe diameter will ensure a fl ow rate of 35,000 gal/min for n 5 1170 r/min?

Two pumps of the type tested in Prob. P11.22 are to be used at 2140 r/min to pump water at 208C vertically upward through 100 m of commercial steel pipe. Should they be in series or in parallel? What is the proper pipe diameter for most effi cient operation?

Consider the axial-fl ow pump of Fig. 11.13, running at 4200 r/min, with an impeller diameter of 36 in. The fl uid is propane gas (molecular weight 44.06). (a) How many pumps in series are needed to increase the gas pressure from 1 atm to 2 atm? (b) Estimate the mass fl ow of gas

Two 32-in pumps from Fig. 11.7a are to be used in series at 1170 r/min to lift water through 500 ft of vertical cast iron pipe. What should the pipe diameter be for most effi - cient operation? Neglect minor losses

Determine if either (a) the smallest or (b) the largest of the seven Taco pumps in Fig. P11.24, running in series at 1160 r/min, can effi ciently pump water at 208C through 1 km of horizontal 12-cm-diameter commercial steel pipe

Reconsider the system of Fig. P6.62. Use the Byron Jackson pump of Prob. P11.28 running at 2134 r/min, no scaling, to drive the fl ow. Determine the resulting fl ow rate between the reservoirs. What is the pump effi ciency?

2 The S-shaped head-versus-fl ow curve in Fig. P11.82 occurs in some axial-fl ow pumps. Explain how a fairly fl at system loss curve might cause instabilities in the operation of the pump. How might we avoid instability? P11.82 H 0 Q

The low-shutoff head-versus-fl ow curve in Fig. P11.83 occurs in some centrifugal pumps. Explain how a fairly fl at system loss curve might cause instabilities in the operation of the pump. What additional vexation occurs when two of these pumps are in parallel? How might we avoid instability?

Turbines are to be installed where the net head is 400 ft and the fl ow rate 250,000 gal/min. Discuss the type, number, and size of turbine that might be selected if the generator selected is (a) 48-pole, 60-cycle (n 5 150 r/min) and (b) 8-pole (n 5 900 r/min). Why are at least two turbines desirable from a planning point of view?

For a high-fl ow site with a head of 45 ft, it is desired to design a single 7-ft-diameter turbine that develops 4000 bhp at a speed of 360 r/min and 88-percent effi ciency. It is decided fi rst to test a geometrically similar model of diameter 1 ft, running at 1180 r/min. (a) What likely type of turbine is in the prototype? What are the appropriate (b) head and (c) fl ow rate for the model test? (d ) Estimate the power expected to be delivered by the model turbine

6 The Tupperware hydroelectric plant on the Blackstone River has four 36-in-diameter turbines, each providing 447 kW at 200 r/min and 205 ft3 /s for a head of 30 ft. What type of turbine are these? How does their performance compare with Fig. 11.22?

An idealized radial turbine is shown in Fig. P11.87. The absolute fl ow enters at 308 and leaves radially inward. The fl ow rate is 3.5 m3 /s of water at 208C. The blade thickness is constant at 10 cm. Compute the theoretical power developed. P11.87 V2 b = 10 cm 30 V1 40 cm 70 cm 1

Performance data for a very small (D 5 8.25 cm) model water turbine, operating with an available head of 49 ft, are as follows: Q, m3 /h 18.7 18.7 18.5 18.3 17.6 16.7 15.1 11.5 RPM 0 500 1000 1500 2000 2500 3000 3500 0 14% 27% 38% 50% 65% 61% 11

A Pelton wheel of 12-ft pitch diameter operates under a net head of 2000 ft. Estimate the speed, power output, and fl ow rate for best effi ciency if the nozzle exit diameter is 4 in

An idealized radial turbine is shown in Fig. P11.90. The absolute fl ow enters at 258 with the blade angles as shown. The fl ow rate is 8 m3 /s of water at 208C. The blade thickness is constant at 20 cm. Compute the theoretical power developed. P11.90 b = 20 cm 1.2 m 35 25 V2 W2 80 r/min W1 30 0.8 m

The fl ow through an axial-fl ow turbine can be idealized by modifying the statorrotor diagrams of Fig. 11.12 for energy absorption. Sketch a suitable blade and fl ow arrangement and the associated velocity vector diagrams.

A dam on a river is being sited for a hydraulic turbine. The fl ow rate is 1500 m3 /h, the available head is 24 m, and the turbine speed is to be 480 r/min. Discuss the estimated turbine size and feasibility for (a) a Francis turbine and (b) a Pelton wheel.

Figure P11.93 shows a cutaway of a cross-fl ow or Banki turbine [55], which resembles a squirrel cage with slotted curved blades. The fl ow enters at about 2 oclock and passes through the center and then again through the blades, leaving at about 8 oclock. Report to the class on the operation and advantages of this design, including idealized velocity vector diagrams

A simple cross-fl ow turbine, Fig. P11.93, was constructed and tested at the University of Rhode Island. The blades were made of PVC pipe cut lengthwise into three 1208-arc pieces. When it was tested in water at a head of 5.3 ft and a fl ow rate of 630 gal/min, the measured power output was 0.6 hp. Estimate (a) the effi ciency and (b) the power specifi c speed if n 5 200 r/min

One can make a theoretical estimate of the proper diameter for a penstock in an impulse turbine installation, as in Fig. P11.95. Let L and H be known, and let the turbine performance be idealized by Eqs. (11.38) and (11.39). Account for friction loss hf in the penstock, but neglect minor losses. Show that (a) the maximum power is generated when hf 5 H/3, (b) the optimum jet velocity is (4gH/3)1/2, and (c) the best nozzle diameter is Dj 5 [D5 /(2 fL)]1/4, where f is the pipe friction factor. Impulse wheel Dj Vj Reservoir Penstock: L, D H P11.95

Apply the results of Prob. P11.95 to determine the optimum (a) penstock diameter and (b) nozzle diameter for a head of 330 m and a fl ow rate of 5400 m3 /h with a cast iron penstock of length 600 m.

Consider the following nonoptimum version of Prob. P11.95: H 5 450 m, L 5 5 km, D 5 1.2 m, Dj 5 20 cm. The penstock is concrete, 5 1 mm. The impulse wheel diameter is 3.2 m. Estimate (a) the power generated by the wheel at 80 percent effi ciency and (b) the best speed of the wheel in r/min. Neglect minor losses.

Francis and Kaplan turbines are often provided with draft tubes, which lead the exit fl ow into the tailwater region, as in Fig. P11.98. Explain at least two advantages in using a draft tube.

Turbines can also cavitate when the pressure at point 1 in Fig. P11.98 drops too low. With NPSH defi ned by Eq. (11.20), the empirical criterion given by Wislicenus [4] for cavitation is Nss 5 (r/min)(gal/min)1/2 3NPSH (ft)4 3/4 $ 11,000 Use this criterion to compute how high z1 2 z2, the impeller eye in Fig. P11.98, can be placed for a Francis turbine with a head of 300 ft, Nsp 5 40, and pa 5 14 lbf/in2 absolute before cavitation occurs in 608F water.

The manufacturer of the wind turbine in the chapteropener photo claims that it develops exactly 100 kW at a wind speed of 15 m/s. Compare this with an estimate from the correlations in Fig. 11.32

A Darrieus VAWT in operation in Lumsden, Saskatchewan, that is 32 ft high and 20 ft in diameter sweeps out an area of 432 ft2 . Estimate (a) the maximum power and (b) the rotor speed if it is operating in 16 mi/h winds

An American 6-ft-diameter multiblade HAWT is used to pump water to a height of 10 ft through 3-in-diameter cast iron pipe. If the winds are 12 mi/h, estimate the rate of water fl ow in gal/min

Only a mile from the wind turbine in the chapter-opener photo is a 100-ft-high, 23-ft-diameter HAWT, in Fig. P11.103. It is rated at 10 kW and provides one-half of the electricity for the Salty Brine State Beach bathhouse. From the data in Fig. 11.32, at a wind velocity of 20 mi/h, estimate (a) the maximum power developed, and (b) the rotation speed, in r/min.

The controversial Cape Cod Wind Project proposes 130 large wind turbines in Nantucket Sound, intended to provide 75 percent of the electric power needs of Cape Cod and the Islands. The turbine diameter is 328 ft. For an average wind velocity of 14 mi/h, what are the best rotation rate and total power output estimates for (a) a HAWT and (b) a VAWT?

In 2007, a wind-powered-vehicle contest, held in North Holland [64], was won with a design by students at the University of Stuttgart. A schematic of the winning threewheeler is shown in Fig. P11.105. It is powered by a shrouded wind turbine, not a propeller, and, unlike a sailboat, can move directly into the wind. (a) How does it work? (b) What if the wind is off to the side? (c) Cite some design questions you might have

6 Analyze the wind-powered-vehicle of Fig. P11.105 with the following data: turbine diameter D 5 6 ft, power coeffi cient (Fig. 11.32) 5 0.3, vehicle CDA 5 4.5 ft2 , and turbine rotation 240 r/min. The vehicle moves directly into a head wind, W 5 25 mi/h. The wind backward thrust on the turbine is approximately T < CT(/2)Vrel2 Aturbine, where Vrel is the air velocity relative to the turbine, and CT < 0.7. Eighty percent of the turbine power is delivered by gears to the wheels, to propel the vehicle. Estimate the sea-level vehicle velocity V, in mi/h

Figure 11.32 showed the typical power performance of a wind turbine. The wind also causes a thrust force that must be resisted by the structure. The thrust coeffi cient CT of a wind turbine may be defi ned as follows: CT 5 Thrust force (/2) AV2 5 T (/2) 3(/4)D2 4 V2 Values of CT for a typical horizontal-axis wind turbine are shown in Fig. P11.107. The abscissa is the same as in Fig. 11.32. Consider the turbine of Prob. P11.103. If the

To avoid the bulky tower and impeller and generator in the HAWT of the chapter-opener photo, we could instead build a number of Darrieus turbines of height 4 m and diameter 3 m. (a) How many of these would we need to match the HAWTs 100 kW output for 15 m/s wind speed and maximum power? (b) How fast would they rotate? Assume the area swept out by a Darrieus turbine is twothirds the height times the diameter