Page 220 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 17] FLUIDS IN MOTION 205

SOLVED PROBLEM 17.8
A barrel 80 cm high is filled with kerosene. When a tap at the bottom of the barrel is opened, with what
velocity does the kerosene emerge?

2
v = 2gh = (2)(9.8 m/s )(0.8m) = 3.96 m/s
SOLVED PROBLEM 17.9

At what velocity should water emerge from the nozzle of a fire hose if it is to reach a height of 80 ft when
the hose is aimed vertically upward?
√
The velocity needed to reach a height h is the same as the velocity v = 2gh that would be acquired in free
fall from that height. Hence

2
v = 2gh = (2)(32 ft/s )(80 ft) = 72 ft/s
SOLVED PROBLEM 17.10
2
A boat strikes an underwater rock that punctures a hole 20 cm in area in its hull 1.5 m below the waterline.
At what rate does water enter the hull?
√
From Torricelli’s theorem, the velocity with which water enters the hull is v = 2gh. Since the rate of flow
√
2
2
through an orifice of area A is R = v A when the fluid velocity is v, R = A 2gh. Here A = 20 cm = 2×10 −3 m ,
so water enters the hull at the rate

−3 2 2 −2 3
R = A 2gh = (2 × 10 m ) (2)(9.8 m/s )(1.5m) = 1.08 × 10 m /s = 108 L/s
This is over 3 tons/min—a serious leak.
SOLVED PROBLEM 17.11
Water flows through the pipe shown in Fig. 17-2 at the rate of 80 L/s. If the pressure at point 1 is 180
kPa, find (a) the velocity at point 1, (b) the velocity at point 2, and (c) the pressure at point 2.

Fig. 17-2

2
(a) Since A = πr and R = v 1 A 1 ,
3
R R (80 L/s)(10 −3 m /L)
v 1 = = 2 = = 0.99 m/s
A 1 πr π(0.16 m) 2
1