fluid_mechanics

246 Chapter 5 ■ Finite Control Volume Analysis
Section 5.1.2 Fixed, Nondeforming Control Volume—
Uniform Velocity Profile or Average Velocity.
5.5 Water enters a cylindrical tank through two pipes at rates of
250 and 100 gal/min (see Fig. P5.5). If the level of the water in the
tank remains constant, calculate the average velocity of the flow
leaving the tank through an 8-in. inside-diameter pipe.
5.8 Water flows into a sink as shown in Video V5.1 and Fig. P5.8
at a rate of 2 gallons per minute. Determine the average velocity
through each of the three 0.4-in.-diameter overflow holes if
the drain is closed and the water level in the sink remains
constant.
Three 0.4–in.-diameter
overflow holes Q = 2 gal/min
Section (1)
Section (2)
Q 2 =
250 gal/min
D 3 = 8 in.
Q 1 =
100 gal/min
Section (3)
Drain
F I G U R E P5.5
5.6 Water flows out through a set of thin, closely spaced blades as
shown in Fig. 5.6 with a speed of V 10 fts around the entire circumference
of the outlet. Determine the mass flowrate through the
inlet pipe.
Inlet
0.08-ft diameter
F I G U R E P5.8
5.9 The wind blows through a 7 ft 10 ft garage door opening
with a speed of 5 fts as shown in Fig. P5.9. Determine the average
speed, V, of the air through the two 3 ft 4 ft openings in the windows.
0.1 ft
V
V
Blades
3 ft 3 ft
0.6 ft
60°
16 ft
10 ft
20°
5 ft/s
V = 10 ft/s
F I G U R E P5.6
5.7 The pump shown in Fig. P5.7 produces a steady flow of 10
gal/s through the nozzle. Determine the nozzle exit diameter, D 2 ,
if the exit velocity is to be V 2 100 fts.
Pump
Section (1)
Section (2)
F I G U R E P5.7
D 2
V 2
22 ft
F I G U R E P5.9
5.10 The human circulatory system consists of a complex branching
pipe network ranging in diameter from the aorta (largest) to the
capillaries (smallest). The average radii and the number of these
vessels is shown in the table below. Does the average blood velocity
increase, decrease, or remain constant as it travels from the aorta
to the capillaries?
Vessel Average Radius, mm Number
Aorta 12.5 1
Arteries 2.0 159
Arterioles 0.03 1.4 10 7
Capillaries 0.006 3.9 10 9