Page 224 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 17] FLUIDS IN MOTION 209

(a) The Reynolds number here is

3
3
dv D (1.0 × 10 kg/m )(1.5 m/s)(3 × 10 −3 m)
N R = = = 4500
η 1.0 × 10 −3 P
2
Since 1 P = 1N·s/m = 1 kg/(m·s), the units cancel, to leave a pure number. Because N R here is greater than
3000, the motion of the water in the tube is turbulent.
(b) The maximum velocity for laminar flow corresponds to a Reynolds number of 2000, so

(1.0 × 10 −3 P)(2000)
ηN R
v max = = = 0.67 m/s
3
3
dD (1.0 × 10 kg/m )(3 × 10 −3 m)
Multiple-Choice Questions

17.1. When a fast train goes through a station, someone standing at the edge of the platform is

(a) pulled toward the train
(b) pushed away from the train
(c) either pulled or pushed, depending on the ratio between the velocity of the train and the velocity of sound
(d) not affected by the train’s passage

17.2. Water leaks out of a hole in the bottom of a water tank. The rate at which water flows out depends on which one or
more of the following?

(a) the density of water
(b) the acceleration of gravity
(c) the area of the hole
(d) the height of the water

17.3. The Reynolds number for fluid flow in a pipe is independent of
(a) the viscosity of the fluid
(b) the velocity of the fluid
(c) the length of the pipe
(d) the diameter of the pipe

17.4. Blood flows at 0.10 L/s through the circulatory system of a person whose capillaries have a total cross-sectional area
2
of 0.25 m . The average velocity of blood in the capillaries is
(a) 0.4 mm/s (c) 25 mm/s
(b) 4 mm/s (d) 40 cm/s

17.5. The average blood pressure of the person in Question 17.4 is 14 kPa. The power developed by the person’s heart,
which beats 1.2 times per second, in pumping blood against this pressure is
(a) 1.2 W (c) 1.7 W
(b) 1.4 W (d) 12 W

17.6. A boiler in which the gauge pressure is 4.0 bar develops a leak. The velocity at which water comes out is
(a) 89 mm/s (c) 28 m/s
(b) 20 m/s (d) 0.80 km/s