Chapter 3 x Integral Relations for a Control Volume
273
3.151 Water flows through a circular
nozzle, exits into the air as a jet, and strikes
a plate. The force required to hold the plate
steady is 70 N. Assuming frictionless onedimensional flow, estimate (a) the velocities
at sections (1) and (2); (b) the mercury manometer reading h.
Solution: (a) First examine the momentum of the jet striking the plate,
¦F
F
§S ·
(998) ¨ ¸ (0.032 )(V22 ) V2
©4¹
70 N
Then V1
Fig. P3.151
U A2V22
m inuin
9.96 m/s
§S ·
(9.96) ¨ ¸ (0.032 )
©4¹
or V1
S
2
(0.1 )
4
V2 A2
A1
Ans. (a)
0.9 m/s
Ans. (a)
(b) Applying Bernoulli,
1
U V22 V12
2
p2 p1
1
(998)(9.962 0.92 ) 49,100 Pa
2
And from our manometry principles,
h
'p
Ug
49,100
| 0.4 m
(133,100 9790)
3.152 A free liquid jet, as in Fig. P3.152,
has constant ambient pressure and small
losses; hence from Bernoulli’s equation
z V 2/(2g) is constant along the jet. For the
fire nozzle in the figure, what are (a) the
minimum and (b) the maximum values of T
for which the water jet will clear the corner
of the building? For which case will the jet
velocity be higher when it strikes the roof
of the building?
Ans. (b)
Fig. P3.152