Problem 11.50
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
P
*
C
for the three pumps of
Prob. 11.49 fit on this correlation. If so, suggest a curve-fitted formula for the data.
Problem 11.49
Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted in
Fig. P11.49. Determine if the values of
Q
*
C
fit this correlation for the three pumps of Problems
P11.28, P11.35, and P11.38. If so, suggest a curve-fitted formula for the data.
Solution 11.50
Make a table of these values, similar to Prob. 11.50:
P*, bhp
D, inches
n, rpm
NS
35
P
*
C P* n D
=()
Prob. 11.28:
255
14.62
2134
1430
0.600
Prob. 11.35:
156
18.0
880
Prob. 11.38:
3500
1400
0.435
Fig. P11.24:
1160
1215
Problem 11.51
An axial-flow pump delivers 40 ft3/s of air that enters at 20C and 1 atm. The flow passage has a
10-in outer radius and an 8-in inner radius. Blade angles are
1 = 60 and
2 = 70, and the rotor
runs at 1800 rpm. For the first stage, compute (a) the head rise; and (b) the power required.
Solution 11.51
Assume an average radius of (8 + 10)/2 = 9 inches and compute the blade speed:
Problem 11.52
An axial-flow 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 = 55 and
1 = 30, while at the outlet
2 = 60.
Estimate the theoretical values of the (a) flow rate, (b) horsepower, and (c) outlet angle
2.
Solution 11.52
For air, take
1.205 kg/m3. The average radius is 0.45 m. Thus
Problem 11.53
Figure P11.46 is an example of a centrifugal pump correlation, where DS is defined in the
problem. We can suggest the following correlation for axial-flow pumps and fans:
0.485
130 for 8000
SS
S
DN
N
where NS is the dimensional specific speed, Eq. (11.30b). Use this correlation to find 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.
Solution 11.53
At sea level, take
air = 1.2255 kg/m3 = 0.00238 slug/ft3.
Convert Q = 24,000 ft3/min = 400 ft3/s = 175,900 gal/min and n = 1620 r/min = 27 r/s. Convert
the head H into feet of air:
Problem 11.54
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.
Solution 11.54
Convert to English units and evaluate the specific speed:
Problem 11.55
Suppose that the axial-flow pump of Fig. 11.13, with D = 18 in, runs at 1800 r/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 ft is desired, what values of D and n would be better?
Solution 11.55
Convert n = 1800 r/min = 30 r/s. The flow coefficient at BEP is approximately 0.55. Check this
against the data:
Problem 11.56
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 r/min.
Problem 11.8
A Bell and Gossett pump at best efficiency, 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 efficiency? (b) What type of
pump is this?
Solution 11.56
Recall the P11.8 data: n = 1750 r/min, H* = 105 ft, Q* = 1050 gal/min, P* = 32.4 hp. Calculate
the specific speed and the specific diameter (from Prob. P11.46):
Problem 11.57
Performance data for a 21–in-diameter air blower running at 3550 rpm are as follows:
p, in H2O:
29
30
28
21
10
Q, ft3/min:
500
1000
2000
3000
4000
bhp:
6
8
12
18
25
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
Q H P
***
C , C , C
?
Solution 11.57
Assume 1-atm air,
0.00233 slug/ft3. Convert the data to dimensionless form and put the
results into a table:
p, psf:
151
156
146
109
52
Problem 11.58
Aircraft propeller specialists claim that dimensionless propeller data, when plotted as (CT/J2)
versus (CP/J2), form a nearly straight line, y = mx + b. (a) Test this hypothesis for the data of
Fig. 11.16, in the high-efficiency range J = V/(nD) equal to 0.6, 0.7, and 0.8. (b) If successful,
500
Q, gal/min:
29920
H, ft (of air):
693
0.0263
0.0526
use this straight line to predict the rotation rate n, in r/min, for a propeller with D = 5 ft,
P = 30 hp, T = 95 lbf, and V = 95 mi/h, for sea-level standard conditions. Comment.
Solution 11.58
For sea-level air, take
= 0.00237 slug/ft3. The writer read Fig. 11.16 as best he could and came
up with the following data, rewritten in the desired form:
Problem 11.59
Suppose it is desired to deliver 700 ft3/min of propane gas (molecular weight = 44.06) at 1 atm
and 20C 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. 11.57 and (b) Fig. 11.13. Which is the better design?
Problem 11.57
Performance data for a 21-in-diameter air blower running at 3550 rpm are as follows:
p, in H2O:
29
30
28
21
10
Q, ft3/min:
500
1000
2000
3000
4000
bhp:
6
8
12
18
25
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
Q H P
* * *
C , C , C
?
Solution 11.59
For propane, with M = 44.06, the gas constant R = 49720/44.06 1128 ftlbf/(slugR). Convert
p = 8 inH2O = (62.4)(8/12) = 41.6 psf. The propane density and head rise are
Problem 11.60
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?
Solution 11.60
(a) The three curves look exactly alike! In fact, we deduce, for this propeller, that the thrust, at
constant speed, is linearly proportional to the horsepower! This implies that the dimensionless
Problem 11.61
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 flow
rate is increased 50 percent for the same diameter, by what percentage will the pressure rise
change?
Solution 11.61
For sea-level air, take
g 11.8 N/m3, hence H = p/
g = 1100/11.8 93 m 305 ft. Convert
500 m3/s to 7.93E6 gal/min and calculate the specific speed:
Problem 11.62
The actual mine-ventilation fan in Prob. 11.61 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?
Problem 11.61
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 flow
rate is increased 50 percent for the same diameter, by what percentage will the pressure rise
change?
Solution 11.62
For sea-level air, take
g 11.8 N/m3. As in Prob. 11.61 above, the specific speed of this fan is
11400, hence an axial-flow fan. Figure 11.14 indicates an efficiency of about 90%, and the only
Problem 11.63
A good curve-fit to the head vs. flow for the 32-inch pump in Fig. 11.7a is
2
(in ft) 500 (2.9 7) , in gal/minH E Q Q − −
Assume the same rotation rate, 1170 r/min, and estimate the flow rate this pump will provide to
deliver water from a reservoir, through 900 ft of 12-inch pipe, to a point 150 ft above the
reservoir surface. Assume a friction factor f = 0.019.
Figure 11.7a:
Solution 11.63
The system head would be the elevation change, 150 ft, plus the friction head loss:
Problem 11.64
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 Eq. (11.27) to drive the blower, what
approximate (a) diameter and (b) rotation speed are appropriate? (c) Is this a good design?
Solution 11.64
Recall that Eq. (11.27) gave BEP coefficients for the pumps of Fig. 11.7:
Problem 11.65*
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 20C 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?
Solution 11.65
For water at 20C, take
= 998 kg/m3 and
= 0.001 kg/m-s. Convert to SI units:
Q = 850 gal/min = 0.0536 m3/s, D = 11.5 in = 0.292 m, H = 105 ft = 32.0 m. Compute ReD
and f:
Problem 11.66
It is proposed to run the pump of Prob. 11.35 at 880 r/min to pump water at 20C through the
system of Fig. P11.66. The pipe is 20-cm diameter commercial steel. What flow rate in ft3/min
results? Is this an efficient operation?
Problem 11.35
An 18-in-diameter centrifugal pump, running at 880 r/min with water at 20C, generates the
following performance data:
Q, gal/min:
0.0
2000
4000
6000
8000
10000
H, ft:
92
89
84
78
68
50
P, hp:
100
112
130
143
156
163
Determine (a) the BEP; (b) the maximum efficiency; and (c) the specific speed. (d) Plot the
required input power versus the flow rate.
Solution 11.66
For water, take
= 998 kg/m3 and
= 0.0010 kg/ms. For commercial steel, take
= 0.046 mm.
Write the energy equation for the system:
Problem 11.67
The pump of Prob. 11.35, running at 880 r/min, is to pump water at 20C through 75 m of
horizontal galvanized-iron pipe. All other system losses are neglected. Determine the flow rate
and input power for (a) pipe diameter = 20 cm; and (b) the pipe diameter yielding maximum
pump efficiency.