fluid_mechanics

144 Chapter 3 ■ Elementary Fluid Dynamics—The Bernoulli Equation
D = 0.15 m
Card
h
0.03-m diameter
Plate
Spool
Tank
p = 1.0 kPa
F I G U R E P3.97
effects and elevation changes are assumed negligible and the flow
exits radially from the circumference of the circular disk with uniform
velocity.
3.98 A conical plug is used to regulate the air flow from the
pipe shown in Fig. P3.98. The air leaves the edge of the cone
with a uniform thickness of 0.02 m. If viscous effects are negligible
and the flowrate is 0.50 m 3 s, determine the pressure
within the pipe.
Pipe
Free jet
V
Q
F I G U R E P3.100
spool with the spool turned upside down. 1Note: It may be necessary
to use a thumb tack to prevent the card from sliding from the
spool.2 Explain this phenomenon.
3.101 Water flows down the sloping ramp shown in Fig. P3.101
with negligible viscous effects. The flow is uniform at sections 112
and 122. For the conditions given, show that three solutions for the
downstream depth, h 2 , are obtained by use of the Bernoulli and continuity
equations. However, show that only two of these solutions
are realistic. Determine these values.
Q = 0.50 m 3 /s
0.23 m
0.20 m
V 1 = 10 ft/s
h 1 = 1 ft
h 2
Cone
H = 2 ft V 2
F I G U R E P3.101
F I G U R E P3.98
0.02 m
3.99 Water flows steadily from a nozzle into a large tank as shown
in Fig. P3.99. The water then flows from the tank as a jet of diameter
d. Determine the value of d if the water level in the tank remains
constant. Viscous effects are negligible.
V
3.102 Water flows in a rectangular channel that is 2.0 m wide as
shown in Fig. P3.102. The upstream depth is 70 mm. The water surface
rises 40 mm as it passes over a portion where the channel bottom
rises 10 mm. If viscous effects are negligible, what is the flowrate?
100 mm
Q
70 mm
10 mm
0.1-ft diameter
4 ft
F I G U R E P3.102
3 ft
d
0.15-ft diameter
*3.103 Water flows up the ramp shown in Fig. P3.103 with negligible
viscous losses. The upstream depth and velocity are maintained at
h 1 0.3 m and V 1 6 m s. Plot a graph of the downstream depth,
h 2 , as a function of the ramp height, H, for 0 H 2 m. Note that
for each value of H there are three solutions, not all of which are realistic.
1 ft
F I G U R E P3.99
3.100 A small card is placed on top of a spool as shown in
Fig. P3.100. It is not possible to blow the card off the spool by
blowing air through the hole in the center of the spool. The harder
one blows, the harder the card “sticks” to the spool. In fact, by
blowing hard enough it is possible to keep the card against the
V 1 = 6 m/s
h 1 = 0.3 m
F I G U R E P3.103
H
h 2
V 2