487
Chapter 6 x Viscous Flow in Ducts
6.81 The pump in Fig. P6.80 is used to deliver gasoline at 20qC through 350 m of
30-cm-diameter galvanized iron pipe. Estimate the resulting flow rate, in m3/s. (Note
that the pump head is now in meters of gasoline.)
Solution: For gasoline, take U
iron, take H | 0.15 mm, hence H/d
hf
8fLQ 2
S 2 gd 5
8f(350)Q 2
S 2 (9.81)(0.3)5
680 kg/m3 and P 2.92E4 kg/m˜s. For galvanized
0.15/300 | 0.0005. Head loss matches pump head:
h pump | 80 20Q 2 , Q 2
11901fQ 2
Guess frough | 0.017, Q | 0.600
Re better | 5.93E6,
H
d
80
20 11901f
m3
,
s
0.0005, fbetter | 0.0168
This converges to f | 0.0168, Re | 5.96E6, Q | 0.603 m3/s. Ans.
6.82 The pump in Fig. P6.80 has its maximum efficiency at a head of 45 m. If it is used
to pump ethanol at 20qC through 200 m of commercial-steel pipe, what is the proper pipe
diameter for maximum pump efficiency?
Solution: For ethanol, take U 789 kg/m3 and P 1.2E3 kg/m˜s. For commercial
steel, take H | 0.046 mm, hence H/d 0.046/(1000d). We know the head and flow rate:
h pump
Then h p
hf
45 m | 80 20Q2 , solve for Q | 1.323 m3 /s.
8fLQ 2
S 2 gd 5
8f(200)(1.323)2
S 2 (9.81)d 5
28.92f
d5
45 m, or: d | 0.915f 1/5
Guess f | 0.02, d | 0.915(0.02)1/5 | 0.419 m,
H
4UQ
Re
| 2.6E6,
| 0.000110
SPd
d
Then fbetter | 0.0130, d better | 0.384 m, Re better | 2.89E6,
H
d
_better | 0.000120
This converges to f | 0.0129, Re | 2.89E6, d | 0.384 m.
Ans.