Page 222 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 17] FLUIDS IN MOTION 207

2
(b) The same procedure is followed here, but first it is necessary to convert 40 lb/in. to its equivalent in pounds
per square foot:
2
lb in.
p 2 − p 1 = 40 144 = 5760 lb/ft 2
in. 2 ft 2
Hence

(2)(5760) lb/ft 2
v 1 = = 77 ft/s
1.94 slugs/ft 3

SOLVED PROBLEM 17.14
A horizontal pipe 1 in. in radius is joined to a pipe 4 in. in radius, as in Fig. 17-3. (a) If the velocity
3
2
of seawater (d = 2.00 slugs/ft ) in the small pipe is 20 ft/s and the pressure there is 30 lb/in. , find
the velocity and pressure in the large pipe. (b) What is the rate of flow through the pipe in pounds
per minute?

4 in.
1 in. 1 2

Fig. 17-3

2
(a) The cross-sectional areas of the pipes are in the same ratio as the squares of their radii, since A = πr . From
v 1 A 1 = v 2 A 2 we obtain
A 1 r 1 2 ft (1in.) 2
v 2 = v 1 = v 1 2 = 20 = 1.25 ft/s
r s (4in.) 2
A 2 2
Because both pipes are horizontal, h 1 = h 2 , and Bernoulli’s equation becomes

lb in. 1 slugs ft ft
2 2 2
2
1

p 2 = p 1 + d v − v 2 = 30 144 + 2 20 − 1.25
2 1 2 in. 2 ft 2 2 ft 3 s s
= 4718 lb/ft 2
which is
4718 lb/ft 2
p 2 = 2 2 = 33 lb/in. 2
144 in. /ft
3
2
2
(b) R = v 1 A 1 = (v 1 )(πr ) = (20 ft/s)(π)( 12 1 ft) = 0.436 ft /s
1
3
Since dg = 64 lb/ft and 1 min = 60 s, the rate of flow in the required units is
3
3
(0.436 ft /s)(64 lb/ft )(60 s/min) = 1674 lb/min
VISCOSITY
The viscosity of a fluid is an internal friction that prevents adjacent layers of the fluid from sliding freely past each
2
other. The symbol of viscosity is η, the Greek letter eta, and its SI unit is the poise (P), where 1 P = 1N·s/m .
The viscosities of liquids decrease with temperature; those of gases increase.