485
Chapter 6 x Viscous Flow in Ducts
6.78 In Fig. P6.78 the connecting pipe is
commercial steel 6 cm in diameter. Estimate
the flow rate, in m3h, if the fluid is water
at 20qC. Which way is the flow?
Solution: For water, take U 998 kgm3
0.001 kgm˜s. For commercial
and P
steel, take H | 0.046 mm, hence Hd
0.04660 | 0.000767. With p1, V1, and V2
all | 0, the energy equation between
surfaces (1) and (2) yields
0 0 z1 |
p2
0 z 2 h f , or h f
Ug
Guess turbulent flow: h f
H
d
f
0.00767, guess ffully rough
fbetter | 0.0204, Vbetter
2.50
L V2
d 2g
Fig. P6.78
15 f
200000
| 5.43 m (flow to left) m
998(9.81)
50 V 2
0.06 2(9.81)
§ 0.1278 ·
| 0.0184, V | ¨
© 0.0184 ¸¹
5.43, or: fV 2 | 0.1278
1/2
| 2.64
m
, Re 158000
s
m
, Re better | 149700, f3rd iteration | 0.0205 (converged)
s
The iteration converges to
f | 0.0205, V | 2.49 ms, Q
(S4)(0.06)2(2.49)
0.00705 m3s
25 m3h m Ans.
6.79 A garden hose is used as the return line in a waterfall display at the mall. In order
to select the proper pump, you need to know the hose wall roughness, which is not
supplied by the manufacturer. You devise a simple experiment: attach the hose to the
drain of an above-ground pool whose surface is 3 m above the hose outlet. You estimate
the minor loss coefficient in the entrance region as 0.5, and the drain valve has a minorloss equivalent length of 200 diameters when fully open. Using a bucket and stopwatch,
you open the valve and measure a flow rate of 2.0E4 m3/s for a hose of inside diameter
1.5 cm and length 10 m. Estimate the roughness height of the hose inside surface.
Solution: First evaluate the average velocity in the hose and its Reynolds number:
V
Q
A
2.0 E4
(S /4)(0.015)2
1.13
m
, Red
s
UVd
P
998(1.13)(0.015)
16940 (turbulent )
0.001