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Fluid Mechanics

Frank M. White

Chapter 11

Turbomachinery - all with Video Answers

Educators

Chapter Questions

02:47

Problem 1

Describe the geometry and operation of a human peristaltic PDP that is cherished by every romantic person on earth. How do the two ventricles differ?

Dennis Howard
Dennis Howard
Numerade Educator
00:37

Problem 2

What would be the technical classification 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 fluid-coupling transmission, and $(g)$ a power plant steam turbine?

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:24

Problem 3

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

Jake Rempel
Jake Rempel
Numerade Educator
03:28

Problem 4

Figure $\mathrm{P} 11.4$ 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?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
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Problem 5

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

Victor Salazar
Victor Salazar
Numerade Educator
01:27

Problem 6

Figure $\mathrm{P} 11.6$ 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 flow rate versus time for a few cycles.

Chai Santi
Chai Santi
Numerade Educator
06:38

Problem 7

A piston PDP has a 5 -in diameter and a 2 -in stroke and operates at $750 \mathrm{r} / \mathrm{min}$ with 92 percent volumetric efficiency. (a) What is its delivery, in gal/min? (b) If the pump delivers SAE $10 \mathrm{W}$ oil at $20^{\circ} \mathrm{C}$ against a head of $50 \mathrm{ft}$, what horsepower is required when the overall efficiency is 84 percent?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:20

Problem 8

A Bell and Gossett pump at best efficiency, running at $1750 \mathrm{r} / \mathrm{min}$ and a brake horsepower of $32.4,$ delivers 1050 gal/min against a head of $105 \mathrm{ft}$ (a) What is its efficiency? (b) What type of pump is this?

Chai Santi
Chai Santi
Numerade Educator
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Problem 9

Figure $\mathrm{P} 11.9$ shows the measured performance of the Vickers model PVQ40 piston pump when delivering SAE $10 \mathrm{W}$ oil at $180^{\circ} \mathrm{F}\left(\rho \approx 910 \mathrm{kg} / \mathrm{m}^{3}\right) .$ Make some general observations about these data vis-à-vis Fig. 11.2 and your intuition about the behavior of piston pumps.

Victor Salazar
Victor Salazar
Numerade Educator
05:06

Problem 10

Suppose that the pump of Fig. P11.9 is run at $1100 \mathrm{r} / \mathrm{min}$ 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 efficiency.

Narayan Hari
Narayan Hari
Numerade Educator
01:43

Problem 11

A pump delivers $1500 \mathrm{L} / \mathrm{min}$ of water at $20^{\circ} \mathrm{C}$ against a pressure rise of 270 kPa. Kinetic and potential energy changes are negligible. If the driving motor supplies $9 \mathrm{kW}$ what is the overall efficiency?

Mayukh Banik
Mayukh Banik
Numerade Educator
07:55

Problem 12

In a test of the centrifugal pump shown in Fig. P11.12, the following data are taken: $p_{1}=100 \mathrm{mmHg}$ (vacuum) and $p_{2}=500 \mathrm{mmHg}$ (gage). The pipe diameters are $D_{1}=12 \mathrm{cm}$ and $D_{2}=5 \mathrm{cm} .$ The flow rate is $180 \mathrm{gal} / \mathrm{min}$ of light oil $(\mathrm{SG}=0.91) .$ Estimate
$(a)$ the head developed, in meters, and $(b)$ the input power required at 75 percent efficiency.

Sanat Mukherjee
Sanat Mukherjee
Numerade Educator
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Problem 13

A 3.5 hp pump delivers 1140 lbf of ethylene glycol at $20^{\circ} \mathrm{C}$ in 12 seconds, against a head of $17 \mathrm{ft}$. Calculate the efficiency of the pump.

Ankur S
Ankur S
Numerade Educator
02:11

Problem 14

A pump delivers gasoline at $20^{\circ} \mathrm{C}$ and $12 \mathrm{m}^{3} / \mathrm{h}$. At the inlet $p_{1}=100 \mathrm{kPa}, z_{1}=1 \mathrm{m},$ and $V_{1}=2 \mathrm{m} / \mathrm{s} .$ At the exit $p_{2}=500 \mathrm{kPa}, z_{2}=4 \mathrm{m},$ and $V_{2}=3 \mathrm{m} / \mathrm{s}$. How much power is required if the motor efficiency is 75 percent?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:39

Problem 15

A lawn sprinkler can be used as a simple turbine. As shown in Fig. $\mathrm{P} 11.15,$ flow enters normal to the paper in the center and splits evenly into $Q / 2$ and $V_{\mathrm{rel}}$ leaving each nozzle. The arms rotate at angular velocity $\omega$ and do work on a shaft. Draw the velocity diagram for this turbine. Neglecting friction, find an expression for the power delivered to the shaft. Find the rotation rate for which the power is a maximum.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
02:57

Problem 16

The centrifugal pump in Fig. P11.16 has $r_{1}=15 \mathrm{cm}$ $r_{2}=25 \mathrm{cm}, b_{1}=b_{2}=6 \mathrm{cm},$ and rotates counterclockwise at $600 \mathrm{r} / \mathrm{min} .$ A sample blade is shown. Assume $\alpha_{1}=90^{\circ}$ Estimate the theoretical flow rate and head produced, for water at $20^{\circ} \mathrm{C},$ and comment.

Chai Santi
Chai Santi
Numerade Educator
04:53

Problem 17

A centrifugal pump has $d_{1}=7$ in, $d_{2}=13$ in, $b_{1}=4$ in, $b_{2}=3$ in, $\beta_{1}=25^{\circ},$ and $\beta_{2}=40^{\circ}$ and rotates at $1160 \mathrm{r} / \mathrm{min}$ If the fluid is gasoline at $20^{\circ} \mathrm{C}$ and the flow enters the blades radially, estimate the theoretical (a) flow rate in gal/min, (b) horsepower, and (c) head in ft.

Narayan Hari
Narayan Hari
Numerade Educator
02:04

Problem 18

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

Chai Santi
Chai Santi
Numerade Educator
01:36

Problem 19

A centrifugal pump has $r_{2}=9$ in, $b_{2}=2$ in, and $\beta_{2}=35^{\circ}$ and rotates at $1060 \mathrm{r} / \mathrm{min}$. If it generates a head of $180 \mathrm{ft}$ determine the theoretical (a) flow rate in $\operatorname{gal} / \min$ and (b) horsepower. Assume near-radial entry flow.

Chai Santi
Chai Santi
Numerade Educator
01:23

Problem 20

Suppose that Prob. P11.19 is reversed into a statement of the theoretical power $P_{w} \approx 153$ hp. Can you then compute the theoretical (a) flow rate and (b) head? Explain and resolve the difficulty that arises.

Chai Santi
Chai Santi
Numerade Educator
02:51

Problem 21

The centrifugal pump of Fig. P11.21 develops a flow rate of 4200 gal/min of gasoline at $20^{\circ} \mathrm{C}$ with near-radial absolute inflow. Estimate the theoretical ( $a$ ) horsepower, $(b)$ head rise, and $(c)$ appropriate blade angle at the inner radius

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 22

A 37 -cm-diameter centrifugal pump, running at $2140 \mathrm{r} / \mathrm{min}$ with water at $20^{\circ} \mathrm{C}$, produces the following performance data:
$$\begin{array}{l|c|c|c|c|c|c|c}
Q, \mathrm{m}^{3} / \mathrm{s} & 0.0 & 0.05 & 0.10 & 0.15 & 0.20 & 0.25 & 0.30 \\
\hline H, \mathrm{m} & 105 & 104 & 102 & 100 & 95 & 85 & 67 \\
\hline P, \mathrm{kW} & 100 & 115 & 135 & 171 & 202 & 228 & 249
\end{array}$$
(a) Determine the best efficiency point. (b) Plot $C_{H}$ versus $C_{Q}$ .(c) If we desire to use this same pump family to deliver 7000 gal/min of kerosene at $20^{\circ} \mathrm{C}$ at an input power of $400 \mathrm{kW},$ what pump speed (in $\mathrm{r} / \mathrm{min}$ ) and impeller size (in $\mathrm{cm}$ ) are needed? What head will be developed?

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 23

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

Chai Santi
Chai Santi
Numerade Educator
02:03

Problem 24

Figure $\mathrm{P} 11.24$ shows performance data for the Taco, Inc. model 4013 pump. Compute the ratios of measured shutoff head to the ideal value $U^{2} / g$ 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.

Chai Santi
Chai Santi
Numerade Educator
02:51

Problem 25

At what speed in r/min should the 35 -in-diameter pump of Fig. $11.7 b$ 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.

Narayan Hari
Narayan Hari
Numerade Educator
01:19

Problem 26

Would the smallest, or the largest, of the seven Taco, Inc. pumps in Fig. $\mathrm{P} 11.24$ be better $(a)$ for producing, near best efficiency, a water flow rate of 600 gal/min and a head of $95 \mathrm{ft} ?(b)$ At what speed, in $\mathrm{r} / \mathrm{min},$ should this pump be run? $(c)$ What input power is required?

Chai Santi
Chai Santi
Numerade Educator
01:22

Problem 27

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

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 28

Tests by the Byron Jackson Co. of a 14.62 -in-diameter centrifugal water pump at $2134 \mathrm{r} / \mathrm{min}$ yield the following data:
$$\begin{array}{l|c|c|c|c|c|c}
Q, \mathrm{ft}^{3} / \mathrm{s} & 0 & 2 & 4 & 6 & 8 & 10 \\
\hline H, \mathrm{ft} & 340 & 340 & 340 & 330 & 300 & 220 \\
\hline \mathrm{bhp} & 135 & 160 & 205 & 255 & 330 & 330
\end{array}$$
What is the BEP? What is the specific speed? Estimate the maximum discharge possible.

Chai Santi
Chai Santi
Numerade Educator
02:48

Problem 29

If the scaling laws are applied to the pump of Prob. P11.28 for the same impeller diameter, determine ( $a$ ) the speed for which the shutoff head will be $280 \mathrm{ft},(b)$ the speed for which the BEP flow rate will be $8.0 \mathrm{ft}^{3} / \mathrm{s}$, and $(c)$ the speed for which the BEP conditions will require 80 hp.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 30

A pump, geometrically similar to the 12.95 -in model in Fig. $P 11.24$, 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 $\mathrm{r} / \mathrm{min} ;(b)$ the BEP head, in $\mathrm{ft}$ and $(c)$ the BEP flow rate, in gal/min.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 31

A centrifugal pump with backward-curved blades has the following measured performance when tested with water at $20^{\circ} \mathrm{C}$:
$$\begin{array}{l|c|c|c|c|c|c|c}
Q, \mathrm{gal} / \mathrm{min} & 0 & 400 & 800 & 1200 & 1600 & 2000 & 2400 \\
\hline \mathrm{H}, \mathrm{ft} & 123 & 115 & 108 & 101 & 93 & 81 & 62 \\
\hline P, \mathrm{hp} & 30 & 36 & 40 & 44 & 47 & 48 & 46
\end{array}$$
(a) Estimate the best efficiency point and the maximum efficiency. (b) Estimate the most efficient flow rate, and the resulting head and brake horsepower, if the diameter is doubled and the rotation speed increased by 50 percent.

Chai Santi
Chai Santi
Numerade Educator
01:15

Problem 32

The data of Prob. P11.31 correspond to a pump speed of $1200 \mathrm{r} / \mathrm{min} .$ (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 $280 \mathrm{ft} ?$

Chai Santi
Chai Santi
Numerade Educator
02:51

Problem 33

In Prob. P11.31, the pump BEP flow 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 find $(a)$ the diameter and ( $b$ ) the speed that will deliver a BEP water flow rate of 4000 gal/min and a head of 180 ft. $(c)$ What brake horsepower will be required for this new condition?

Narayan Hari
Narayan Hari
Numerade Educator
01:19

Problem 34

You are asked to consider a pump geometrically similar to the 9 -in-diameter Taco pump of Fig. $\mathrm{P} 11.34$ to deliver 1200 gal/min at $1500 \mathrm{r} / \mathrm{min} .$ Determine the appropriate (a) impeller diameter (b) BEP horsepower (c) shutoff head, and (d) maximum efficiency. The fluid is kerosene, not water.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 35

An 18 -in-diameter centrifugal pump, running at $880 \mathrm{r} / \mathrm{min}$ with water at $20^{\circ} \mathrm{C}$, generates the following performance data:
$$\begin{array}{l|c|c|c|c|c|c}
Q, \mathrm{gal} / \mathrm{min} & 0.0 & 2000 & 4000 & 6000 & 8000 & 10,000 \\
\hline H, \mathrm{ft} & 92 & 89 & 84 & 78 & 68 & 50 \\
\hline P, \mathrm{hp} & 100 & 112 & 130 & 143 & 156 & 163
\end{array}$$
Determine $(a)$ the $\mathrm{BEP},(b)$ the maximum efficiency, and $(c)$ the specific speed. $(d)$ Plot the required input power versus the flow rate.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 36

The pump of Prob. P11.35 has a maximum efficiency 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 $150 \mathrm{ft}$ and a BEP flow rate of $10,000 \mathrm{gal} / \mathrm{min} ?(b)$ If not, what diameter is appropriate?

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 37

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?

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 38

A 6.85 -in pump, running at $3500 \mathrm{r} / \mathrm{min}$, has the following measured performance for water at $20^{\circ} \mathrm{C}$:
$$\begin{array}{l|c|c|c|c|c|c|c|c|c}
Q, \text { gal/min } & 50 & 100 & 150 & 200 & 250 & 300 & 350 & 400 & 450 \\
\hline H, \mathrm{ft} & 201 & 200 & 198 & 194 & 189 & 181 & 169 & 156 & 139 \\
\hline \eta, \% & 29 & 50 & 64 & 72 & 77 & 80 & 81 & 79 & 74
\end{array}$$
(a) Estimate the horsepower at BEP. If this pump is rescaled in water to provide 20 bhp at $3000 \mathrm{r} / \mathrm{min}$, determine the appropriate ( $b$ ) impeller diameter, $(c)$ flow rate, and $(d)$ efficiency for this new condition.

Chai Santi
Chai Santi
Numerade Educator
02:16

Problem 39

The Allis-Chalmers D30LR centrifugal compressor delivers $33,000 \mathrm{ft}^{3} / \mathrm{min}$ of $\mathrm{SO}_{2}$ with a pressure change from 14.0 to $18.0 \mathrm{lbf} / \mathrm{in}^{2}$ absolute using an 800 -hp motor at $3550 \mathrm{r} / \mathrm{min}$ What is the overall efficiency? What will the flow rate and $\Delta p$ be at $3000 \mathrm{r} / \mathrm{min} ?$ Estimate the diameter of the impeller.

Narayan Hari
Narayan Hari
Numerade Educator
01:15

Problem 40

The specific speed $N_{s},$ as defined by Eqs. $(11.30),$ does not contain the impeller diameter. How then should we size the pump for a given $N_{s} ?$ An alternate parameter is the specific diameter, $D_{s},$ which is a dimensionless combination of $Q, g H$ and $D$ $(a)$ If $D_{s}$ is proportional to $D,$ determine its form. (b) What is the relationship, if any, of $D_{s}$ to $C_{Q^{*}}, C_{H^{*}},$ and $C_{P^{*}} ?$ $(c)$ Estimate $D_{s}$ for the two pumps of Figs. 11.8 and 11.13.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 41

It is desired to build a centrifugal pump geometrically similar to that of Prob. P11.28 to deliver 6500 gal/min of gasoline at $20^{\circ} \mathrm{C}$ at $1060 \mathrm{r} / \mathrm{min}$. Estimate the resulting $(a)$ impeller diameter, $(b)$ head $(c)$ brake horsepower, and $(d)$ maximum efficiency.

Chai Santi
Chai Santi
Numerade Educator
05:32

Problem 42

An 8 -in model pump delivering $180^{\circ} \mathrm{F}$ water at $800 \mathrm{gal} / \mathrm{min}$ and $2400 \mathrm{r} / \mathrm{min}$ begins to cavitate when the inlet pressure and velocity are 12 lbf/in $^{2}$ absolute and $20 \mathrm{ft} / \mathrm{s}$, respectively. Find the required NPSH of a prototype that is 4 times larger and runs at $1000 \mathrm{r} / \mathrm{min}$.

Saurabh Kumar Gupta
Saurabh Kumar Gupta
Numerade Educator
01:20

Problem 43

The 28 -in-diameter pump in Fig. $11.7 a$ at $1170 \mathrm{r} / \mathrm{min}$ is used to pump water at $20^{\circ} \mathrm{C}$ through a piping system at $14,000 \mathrm{gal} / \mathrm{min}$ (a) Determine the required brake horsepower. The average friction factor is 0.018 . ( $b$ ) If there is $65 \mathrm{ft}$ of 12 -in-diameter pipe upstream of the pump, how far below the surface should the pump inlet be placed to avoid cavitation?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:39

Problem 44

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

Narayan Hari
Narayan Hari
Numerade Educator
02:03

Problem 45

Determine the specific 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?

Chai Santi
Chai Santi
Numerade Educator
01:15

Problem 46

The answer to Prob. P11.40 is that the dimensionless "specific diameter" takes the form $D_{s}=D\left(g H^{*}\right)^{1 / 4} / Q^{* 1 / 2}$ evaluated at the BEP. Data collected by the author for 30 different pumps indicate, in Fig. P11.46, that $D_{s}$ correlates well with specific speed $N_{s}$. Use this figure 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 $1200 \mathrm{r} / \mathrm{min} .$ Suggest a curve-fitted formula to the data. Hint: Use a hyperbolic formula.

Chai Santi
Chai Santi
Numerade Educator
03:52

Problem 47

A pump must be designed to deliver $6 \mathrm{m}^{3} / \mathrm{s}$ of water against a head of $28 \mathrm{m}$. The specified shaft speed is $20 \mathrm{r} / \mathrm{s}$. What type of pump do you recommend?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:36

Problem 48

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

Chai Santi
Chai Santi
Numerade Educator
01:15

Problem 49

Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted versus specific 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 fit on this correlation. If so, suggest a curve-fitted formula for the data.

Chai Santi
Chai Santi
Numerade Educator
01:15

Problem 50

Data collected by the author for power coefficient at BEP for 30 different pumps are plotted versus specific speed in Fig. P11.50. Determine if the values of $C_{P}^{*}$ for the three pumps in Prob. P11.49 also fit on this correlation. If so, suggest a curve-fitted formula for the data.

Chai Santi
Chai Santi
Numerade Educator
04:00

Problem 51

An axial-flow blower delivers $40 \mathrm{ft}^{3} / \mathrm{s}$ of air that enters at $20^{\circ} \mathrm{C}$ and 1 atm. The flow passage has a 10 -in outer radius and an 8 -in inner radius. Blade angles are $\alpha_{1}=60^{\circ}$ and $\beta_{2}=70^{\circ},$ and the rotor runs at $1800 \mathrm{r} / \mathrm{min} .$ For the first stage compute ( $a$ ) the head rise and $(b)$ the power required.

Chai Santi
Chai Santi
Numerade Educator
04:00

Problem 52

An axial-flow fan operates in sea-level air at $1200 \mathrm{r} / \mathrm{min}$ and has a blade-tip diameter of $1 \mathrm{m}$ and a root diameter of $80 \mathrm{cm} .$ The inlet angles are $\alpha_{1}=55^{\circ}$ and $\beta_{1}=30^{\circ},$ while at the outlet $\beta_{2}=60^{\circ} .$ Estimate the theoretical values of the (a) flow rate (b) horsepower, and (c) outlet angle $\alpha_{2}$.

Chai Santi
Chai Santi
Numerade Educator
02:09

Problem 53

Figure $\mathrm{P} 11.46$ is an example of a centrifugal pump correlation, where $D_{s}$ is defined in the problem. From data in the literature, we can suggest the following correlation for axial-flow pumps and fans: $$D_{s} \approx \frac{130}{N_{s}^{0.485}} \quad \text { for } N_{s}>8000$$ where $N_{s}$ is the dimensional specific speed, Eq. $(11.30 b)$ Use this correlation to find the appropriate size for a fan that delivers $24,000 \mathrm{ft}^{3} / \mathrm{min}$ of air at sea-level conditions when running at $1620 \mathrm{r} / \mathrm{min}$ with a pressure rise of 2 inches of water. Hint: Express the fan head in feet of air, not feet of water.

Penny Riley
Penny Riley
Numerade Educator
04:53

Problem 54

It is desired to pump $50 \mathrm{ft}^{3} / \mathrm{s}$ of water at a speed of $22 \mathrm{r} / \mathrm{s}$ against a head of $80 \mathrm{ft}$. ( $a$ ) What type of pump would you recommend? Estimate $(b)$ the required impeller diameter and $(c)$ the brake horsepower.

Narayan Hari
Narayan Hari
Numerade Educator
03:20

Problem 55

Suppose that the axial-flow pump of Fig. $11.13,$ with $D=$ 18 in, runs at $1800 \mathrm{r} / \mathrm{min}$
$(a)$ Could it efficiently pump 25,000 gal/min of water? ( $b$ ) If so, what head would result? $(c)$ If a head of $120 \mathrm{ft}$ is desired, what values of $D$ and $n$ would be better?

Chai Santi
Chai Santi
Numerade Educator
01:15

Problem 56

Determine if the Bell and Gossett pump of Prob. P11.8 (a) fits the three correlations in Figs. P11.46, P11.49, and P11.50. (b) If so, use these correlations to find the flow rate and horsepower that would result if the pump is scaled up to $D=24$ in but still runs at $1750 \mathrm{r} / \mathrm{min}$.

Chai Santi
Chai Santi
Numerade Educator
01:19

Problem 57

Performance data for a 21 -in-diameter air blower running at $3550 \mathrm{r} / \mathrm{min}$ are as follows:
$$\begin{array}{l|c|c|c|c|c}
\Delta p, \text { in } \mathrm{H}_{2} \mathrm{O} & 29 & 30 & 28 & 21 & 10 \\
\hline Q, \mathrm{ft}^{3} / \mathrm{min} & 500 & 1000 & 2000 & 3000 & 4000 \\
\hline \text { bhp } & 6 & 8 & 12 & 18 & 25
\end{array}$$
Note the fictitious expression of pressure rise in terms of water rather than air. What is the specific speed? How does the performance compare with Fig. $11.8 ?$ What are $C_{Q}^{*}, C_{H}^{*}$ and $C_{P}^{*} ?$

Chai Santi
Chai Santi
Numerade Educator
06:19

Problem 58

Aircraft propeller specialists claim that dimensionless propeller data, when plotted as $\left(C_{T} / J^{2}\right)$ versus $\left(C_{P} / J^{2}\right),$ form a nearly straight line, $y=m x+b .(a)$ Test this hypothesis for the data of Fig. $11.16,$ in the high efficiency range $J=V /(n D)$ equal to $0.6,0.7,$ and $0.8 .(b)$ If successful, try this straight line to predict the rotation rate, in $\mathrm{r} / \mathrm{min},$ for a propeller with $D=5 \mathrm{ft}, P=30 \mathrm{hp}, T=95 \mathrm{lbf},$ and $V=95 \mathrm{mi} / \mathrm{h},$ for sea level standard conditions. Comment.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:21

Problem 59

Suppose it is desired to deliver $700 \mathrm{ft}^{3} / \mathrm{min}$ of propane gas (molecular weight $=44.06$ ) at 1 atm and $20^{\circ} \mathrm{C}$ with a single-stage pressure rise of 8.0 in $\mathrm{H}_{2} \mathrm{O}$. Determine the appropriate size and speed for using the pump families of $(a)$ Prob. $P 11.57$ and (b) Fig. $11.13 .$ Which is the better design?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
04:47

Problem 60

Performance curves for a certain free propeller, comparable to Fig. $11.16,$ can be plotted as shown in Fig. $\mathrm{P} 11.60$ 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. $11.16 ?$

Chai Santi
Chai Santi
Numerade Educator
04:29

Problem 61

A mine ventilation fan, running at $295 \mathrm{r} / \mathrm{min}$, delivers $500 \mathrm{m}^{3} / \mathrm{s}$ of sea-level air with a pressure rise of $1100 \mathrm{Pa}$ Is this fan axial, centrifugal, or mixed? Estimate its diameter in $\mathrm{ft}$. If the flow rate is increased 50 percent for the same diameter, by what percentage will the pressure rise change?

Narayan Hari
Narayan Hari
Numerade Educator
02:16

Problem 62

The actual mine ventilation fan discussed in Prob. P11.61 had a diameter of $20 \mathrm{ft}$ [Ref. $20, \mathrm{p.} 339$ ]. What would be the proper diameter for the pump family of Fig. 11.14 to provide $500 \mathrm{m}^{3} / \mathrm{s}$ at $295 \mathrm{r} / \mathrm{min}$ and $\mathrm{BEP} ?$ What would be the resulting pressure rise in Pa?

Averell Hause
Averell Hause
Carnegie Mellon University
View

Problem 63

A good curve-fit to the head vs. flow for the 32 -in pump in Fig. $11.7 a$ is
$$
H(\text { in } \mathrm{ft}) \approx 500-(2.9 \mathrm{E}-7) Q^{2} \quad Q \text { in gal/min }
$$ Assume the same rotation rate, $1170 \mathrm{r} / \mathrm{min},$ and estimate the flow rate this pump will provide to deliver water from a reservoir, through 900 ft of 12 -in pipe, to a point $150 \mathrm{ft}$ above the reservoir surface. Assume a friction factor $f=0.019$.

Victor Salazar
Victor Salazar
Numerade Educator
02:07

Problem 64

A leaf blower is essentially a centrifugal impeller exiting to a tube. Suppose that the tube is smooth PVC pipe, $4 \mathrm{ft}$ long, with a diameter of 2.5 in. The desired exit velocity is $73 \mathrm{mi} / \mathrm{h}$ 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?

Chai Santi
Chai Santi
Numerade Educator
04:53

Problem 65

An 11.5-in-diameter centrifugal pump, running at $1750 \mathrm{r} / \mathrm{min},$ delivers $850 \mathrm{gal} / \mathrm{min}$ and a head of $105 \mathrm{ft}$ at best efficiency ( 82 percent). ( $a$ ) Can this pump operate efficiently when delivering water at $20^{\circ} \mathrm{C}$ through $200 \mathrm{m}$ 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 $/ \mathrm{min} ?$

Narayan Hari
Narayan Hari
Numerade Educator
19:46

Problem 66

It is proposed to run the pump of Prob. P11.35 at $880 \mathrm{r} / \mathrm{min}$ to pump water at $20^{\circ} \mathrm{C}$ through the system in Fig. $\mathrm{P} 11.66$ The pipe is 20 -cm-diameter commercial steel. What flow rate in $\mathrm{ft}^{3} / \mathrm{min}$ will result? Is this an efficient application?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
19:46

Problem 67

The pump of Prob. P11.35, running at $880 \mathrm{r} / \mathrm{min}$, is to pump water at $20^{\circ} \mathrm{C}$ through $75 \mathrm{m}$ of horizontal galvanized iron pipe. All other system losses are neglected. Determine the flow rate and input power for $(a)$ pipe diameter $=$ $20 \mathrm{cm}$ and $(b)$ the pipe diameter found to yield maximum pump efficiency.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:36

Problem 68

A popular small aircraft cruises at $230 \mathrm{km} / \mathrm{h}$ at $8500 \mathrm{ft}$ altitude. It weighs 2200 lbf, has a 180 -hp engine, a 76-in-diameter propeller, and a drag-area $C_{D} A \approx 5.6 \mathrm{ft}^{2}$ The propeller data in Fig. $\mathrm{P} 11.68$ is proposed to drive this aircraft. Estimate the required rotation rate, in $\mathrm{r} / \mathrm{min},$ and power delivered, in hp. [NOTE: Simply use the coefficient pairs. The actual advance ratio is too high.]

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:51

Problem 69

The pump of Prob. P11.38, running at $3500 \mathrm{r} / \mathrm{min},$ is used to deliver water at $20^{\circ} \mathrm{C}$ through $600 \mathrm{ft}$ of cast iron pipe to an elevation $100 \mathrm{ft}$ higher. Determine $(a)$ the proper pipe diameter for BEP operation and ( $b$ ) the flow rate that results if the pipe diameter is 3 in.

Narayan Hari
Narayan Hari
Numerade Educator
02:59

Problem 70

The pump of Prob. P11.28, operating at 2134 r/min, is used with $20^{\circ} \mathrm{C}$ water in the system of Fig. $\mathrm{P} 11.70 .(a)$ If it is operating at BEP, what is the proper elevation $z_{2} ?(b)$ If $z_{2}=225 \mathrm{ft},$ what is the flow rate if $d=8$ in.?

Chai Santi
Chai Santi
Numerade Educator
04:15

Problem 71

The pump of Prob. P11.38, running at 3500 r/min, delivers water at $20^{\circ} \mathrm{C}$ through $7200 \mathrm{ft}$ of horizontal 5 -in-diameter commercial steel pipe. There are a sharp entrance, sharp exit, four $90^{\circ}$ elbows, and a gate valve. Estimate $(a)$ the flow 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 $10 \not c /\mathrm{kWh}$.

Chai Santi
Chai Santi
Numerade Educator
02:59

Problem 72

Performance data for a small commercial pump are as follows:
$$\begin{array}{l|c|c|c|c|c|c|c|c}
Q, \mathrm{gal} / \mathrm{min} & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 \\
\hline H, \mathrm{ft} & 75 & 75 & 74 & 72 & 68 & 62 & 47 & 24
\end{array}$$
This pump supplies $20^{\circ} \mathrm{C}$ water to a horizontal $\frac{5}{8}$ -in-diameter garden hose $(\varepsilon \approx 0.01 \text { in })$ that is 50 ft long. Estimate $(a)$ the flow rate and $(b)$ the hose diameter that would cause the pump to operate at BEP.

Chai Santi
Chai Santi
Numerade Educator
02:17

Problem 73

The Bell and Gossett pump of Prob. P11.8, running under the same conditions, delivers water at $20^{\circ} \mathrm{C}$ through a long, smooth, 8 -in-diameter pipe. Neglect minor losses. How long is the pipe?

James Kiss
James Kiss
Numerade Educator
03:28

Problem 74

The 32 -in pump in Fig. $11.7 a$ is used at $1170 \mathrm{r} / \mathrm{min}$ in a system whose head curve is $H_{s}(\mathrm{ft})=100+1.5 Q^{2},$ 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 configuration is best?

Narayan Hari
Narayan Hari
Numerade Educator
04:48

Problem 75

Two 35 -in pumps from Fig. $11.7 b$ are installed in parallel for the system of Fig. P11.75. Neglect minor losses. For water at $20^{\circ} \mathrm{C},$ estimate the flow rate and power required if $(a)$ both pumps are running and ( $b$ ) one pump is shut off and isolated.

Ameer Said
Ameer Said
Numerade Educator
01:31

Problem 76

Two 32 -in pumps from Fig. $11.7 a$ are combined in parallel to deliver water at $60^{\circ} \mathrm{F}$ through $1500 \mathrm{ft}$ of horizontal pipe. If $f=0.025,$ what pipe diameter will ensure a flow rate of 35,000 gal/min for $n=1170 \mathrm{r} / \mathrm{min} ?$

Penny Riley
Penny Riley
Numerade Educator
01:31

Problem 77

Two pumps of the type tested in Prob. $P 11.22$ are to be used at $2140 \mathrm{r} / \mathrm{min}$ to pump water at $20^{\circ} \mathrm{C}$ vertically upward through $100 \mathrm{m}$ of commercial steel pipe. Should they be in series or in parallel? What is the proper pipe diameter for most efficient operation?

Penny Riley
Penny Riley
Numerade Educator
06:28

Problem 78

Consider the axial-flow pump of Fig. $11.13,$ running at $4200 \mathrm{r} / \mathrm{min},$ with an impeller diameter of 36 in. The fluid 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 flow of gas.

Shahab Ullah
Shahab Ullah
Numerade Educator
01:31

Problem 79

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

Penny Riley
Penny Riley
Numerade Educator
01:31

Problem 80

Determine if either $(a)$ the smallest or $(b)$ the largest of the seven Taco pumps in Fig. P11.24, running in series at $1160 \mathrm{r} / \mathrm{min},$ can efficiently pump water at $20^{\circ} \mathrm{C}$ through $\mathrm{km}$ of horizontal 12 -cm-diameter commercial steel pipe.

Penny Riley
Penny Riley
Numerade Educator
02:46

Problem 81

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 flow. Determine the resulting flow rate between the reservoirs. What is the pump efficiency?

Chai Santi
Chai Santi
Numerade Educator
01:51

Problem 82

The S-shaped head-versus-flow curve in Fig. P11.82 occurs in some axial-flow pumps. Explain how a fairly flat system loss curve might cause instabilities in the operation of the pump. How might we avoid instability?

Chai Santi
Chai Santi
Numerade Educator
01:39

Problem 83

The low-shutoff head-versus-flow curve in Fig. $\mathrm{P} 11.83$ occurs in some centrifugal pumps. Explain how a fairly flat 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?

Narayan Hari
Narayan Hari
Numerade Educator
01:36

Problem 84

Turbines are to be installed where the net head is $400 \mathrm{ft}$ and the flow 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 $(n=150 \mathrm{r} / \mathrm{min})$ and (b) 8 -pole $(n=$ $900 \mathrm{r} / \mathrm{min}$ ). Why are at least two turbines desirable from a planning point of view?

Penny Riley
Penny Riley
Numerade Educator
03:37

Problem 85

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

Chai Santi
Chai Santi
Numerade Educator
01:05

Problem 86

The Tupperware hydroelectric plant on the Blackstone River has four 36 -in-diameter turbines, each providing $447 \mathrm{kW}$ at $200 \mathrm{r} / \mathrm{min}$ and $205 \mathrm{ft}^{3} / \mathrm{s}$ for a head of $30 \mathrm{ft}$. What type of turbine are these? How does their performance compare with Fig. $11.22 ?$

Chai Santi
Chai Santi
Numerade Educator
View

Problem 87

An idealized radial turbine is shown in Fig. P11.87. The absolute flow enters at $30^{\circ}$ and leaves radially inward. The flow rate is $3.5 \mathrm{m}^{3} / \mathrm{s}$ of water at $20^{\circ} \mathrm{C}$. The blade thickness is constant at $10 \mathrm{cm} .$ Compute the theoretical power developed.

Victor Salazar
Victor Salazar
Numerade Educator
01:32

Problem 88

Performance data for a very small ( $D=8.25 \mathrm{cm}$ ) model water turbine, operating with an available head of $49 \mathrm{ft}$, are as follows:
$$\begin{array}{l|c|c|c|c|c|c|c|c}
Q, \mathrm{m}^{3} / \mathrm{h} & 18.7 & 18.7 & 18.5 & 18.3 & 17.6 & 16.7 & 15.1 & 11.5 \\
\hline \mathrm{RPM} & 0 & 500 & 1000 & 1500 & 2000 & 2500 & 3000 & 3500 \\
\hline \eta & 0 & 14 \% & 27 \% & 38 \% & 50 \% & 65 \% & 61 \% & 11 \%
\end{array}$$
(a) What type of turbine is this likely to be? ( $b$ ) What is so different about these data compared to the dimensionless performance plot in Fig. $11.22 d ?$ Suppose it is desired to use a geometrically similar turbine to serve where the available head and flow are $150 \mathrm{ft}$ and $6.7 \mathrm{ft}^{3} / \mathrm{s}$, respectively. Estimate the most efficient ( $c$ ) turbine diameter, (d) rotation speed, and $(e)$ horsepower.

Dominador Tan
Dominador Tan
Numerade Educator
02:56

Problem 89

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

Chai Santi
Chai Santi
Numerade Educator
01:40

Problem 90

An idealized radial turbine is shown in Fig. P11.90. The absolute flow enters at $25^{\circ}$ with the blade angles as shown. The flow rate is $8 \mathrm{m}^{3} / \mathrm{s}$ of water at $20^{\circ} \mathrm{C}$. The blade thickness is constant at $20 \mathrm{cm} .$ Compute the theoretical power developed.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
04:17

Problem 91

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

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:36

Problem 92

A dam on a river is being sited for a hydraulic turbine. The flow rate is $1500 \mathrm{m}^{3} / \mathrm{h}$, the available head is $24 \mathrm{m},$ and the turbine speed is to be $480 \mathrm{r} / \mathrm{min}$. Discuss the estimated turbine size and feasibility for $(a)$ a Francis turbine and $(b)$ a Pelton wheel.

Penny Riley
Penny Riley
Numerade Educator
04:17

Problem 93

Figure $\mathrm{P} 11.93$ shows a cutaway of a cross-flow or "Banki" turbine $[55],$ which resembles a squirrel cage with slotted curved blades. The flow enters at about 2 o'clock and passes through the center and then again through the blades, leaving at about 8 o'clock. Report to the class on the operation and advantages of this design, including idealized velocity vector diagrams.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:55

Problem 94

A simple cross-flow 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 $120^{\circ}$ -arc pieces. When it was tested in water at a head of $5.3 \mathrm{ft}$ and a flow rate of 630 gal/min, the measured power output was 0.6 hp. Estimate $(a)$ the efficiency and
$(b)$ the power specific speed if $n=200 \mathrm{r} / \mathrm{min}$.

Chai Santi
Chai Santi
Numerade Educator
12:53

Problem 95

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 $h_{f}$ in the penstock, but neglect minor losses. Show that $(a)$ the maximum power is generated when $h_{f}=H / 3,(b)$ the optimum jet velocity is $(4 g H / 3)^{1 / 2}$ and $(c)$ the best nozzle diameter is $D_{j}=\left[D^{5} /(2 f L)\right]^{1 / 4},$ where $f$ is the pipe friction factor.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:10

Problem 96

Apply the results of Prob. P1 1.95 to determine the optimum (a) penstock diameter and (b) nozzle diameter for a head of $330 \mathrm{m}$ and a flow rate of $5400 \mathrm{m}^{3} / \mathrm{h}$ with a cast iron penstock of length $600 \mathrm{m}$.

Dominador Tan
Dominador Tan
Numerade Educator
05:38

Problem 97

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

Shoukat Ali
Shoukat Ali
Other Schools
01:49

Problem 98

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

Narayan Hari
Narayan Hari
Numerade Educator
02:41

Problem 99

Turbines can also cavitate when the pressure at point 1 in Fig. $\mathrm{P} 11.98$ drops too low. With NPSH defined by Eq. $(11.20),$ the empirical criterion given by Wislicenus [4] for cavitation is
\[
N_{s s}=\frac{(\mathrm{r} / \mathrm{min})(\mathrm{gal} / \mathrm{min})^{1 / 2}}{[\mathrm{NPSH}(\mathrm{ft})]^{3 / 4}} \geq 11,000
\]
Use this criterion to compute how high $z_{1}-z_{2},$ the impeller eye in Fig. $\mathrm{P} 11.98$, can be placed for a Francis turbine with a head of $300 \mathrm{ft}, N_{s p}=40,$ and $p_{a}=14 \mathrm{lbf} / \mathrm{in}^{2}$ absolute
before cavitation occurs in $60^{\circ} \mathrm{F}$ water.

Amit Srivastava
Amit Srivastava
Numerade Educator
01:15

Problem 100

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

Michael Jacobsen
Michael Jacobsen
Numerade Educator
01:35

Problem 101

A Darrieus VAWT in operation in Lumsden, Saskatchewan, that is $32 \mathrm{ft}$ high and $20 \mathrm{ft}$ in diameter sweeps out an area of $432 \mathrm{ft}^{2}$. Estimate $(a)$ the maximum power and $(b)$ the rotor speed if it is operating in $16 \mathrm{mi} / \mathrm{h}$ winds.

Chai Santi
Chai Santi
Numerade Educator
02:10

Problem 102

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

Daphne Pusey
Daphne Pusey
Numerade Educator
02:33

Problem 103

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 $10 \mathrm{kW}$ 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 $20 \mathrm{mi} / \mathrm{h}$ estimate ( $a$ ) the maximum power developed, and ( $b$ ) the rotation speed, in $\mathrm{r} / \mathrm{min}$.

Taylor Shimono
Taylor Shimono
Numerade Educator
05:24

Problem 104

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 $14 \mathrm{mi} / \mathrm{h},$ what are the best rotation rate and total power output estimates for $(a)$ a HAWT and $(b)$ a VAWT?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:10

Problem 105

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 three-wheeler 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.

Raj Bala
Raj Bala
Numerade Educator
01:10

Problem 106

Analyze the wind-powered-vehicle of Fig. P11.105 with the following data: turbine diameter $D=6 \mathrm{ft}$, power coefficient (Fig. $11.32)=0.3,$ vehicle $C_{D} A=4.5 \mathrm{ft}^{2},$ and turbine rotation $240 \mathrm{r} / \mathrm{min}$. The vehicle moves directly into a head wind, $W=25 \mathrm{mi} / \mathrm{h}$. The wind backward thrust on the turbine is approximately $T \approx C_{T}(\rho / 2) V_{\mathrm{rel}}^{2} A_{\text {turbine }}$ where $V_{\mathrm{rel}}$ is the air velocity relative to the turbine, and $C_{T} \approx 0.7 .$ 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 $\mathrm{mi} / \mathrm{h}$.

Raj Bala
Raj Bala
Numerade Educator
01:10

Problem 107

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 coefficient $C_{T}$ of a wind turbine may be defined as follows:
\[
C_{T}=\frac{\text {Thrust force}}{(\rho / 2) A V^{2}}=\frac{T}{(\rho / 2)\left[(\pi / 4) D^{2}\right] V^{2}}
\]
Values of $C_{T}$ for a typical horizontal-axis wind turbine are shown in Fig. $\mathrm{P} 11.107 .$ The abscissa is the same as in Fig. $11.32 .$ Consider the turbine of Prob. P11.103. If the wind is $20 \mathrm{mi} / \mathrm{h}$ and the rotation rate $115 \mathrm{r} / \mathrm{min}$, estimate the bending moment about the tower base.

Raj Bala
Raj Bala
Numerade Educator
03:01

Problem 108

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 $4 \mathrm{m}$ and diameter $3 \mathrm{m}$ (a) How many of these would we need to match the HAWT's $100 \mathrm{kW}$ output for $15 \mathrm{m} / \mathrm{s}$ 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.

Shahab Ullah
Shahab Ullah
Numerade Educator