fluid_mechanics

Problems 143
opened and the pond is allowed to drain through a pipe of diameter D.
If viscous effects are negligible and quasisteady conditions are assumed,
plot the water depth as a function of time from when the valve
is opened 1t 02 until the pond is drained for pipe diameters of
D 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 ft. Assume h 18 ft at t 0.
3.94 Water flows from a large tank through a large pipe that splits
into two smaller pipes as shown in Fig. P3.94. If viscous effects are
negligible, determine the flowrate from the tank and the pressure at
point 112.
Area A
3 m
h
3 ft
7 m
0.03-m diameter
0.05-m diameter
F I G U R E P3.91
h (ft) A [acres (1 acre 43,560 ft 2 )]
0 0
2 0.3
4 0.5
6 0.8
8 0.9
10 1.1
12 1.5
14 1.8
16 2.4
18 2.8
D
(1)
F I G U R E P3.94
0.02-m diameter
3.95 An air cushion vehicle is supported by forcing air into the
chamber created by a skirt around the periphery of the vehicle as
shown in Fig. P3.95. The air escapes through the 3-in. clearance between
the lower end of the skirt and the ground (or water). Assume
the vehicle weighs 10,000 lb and is essentially rectangular in shape,
30 by 65 ft. The volume of the chamber is large enough so that the
kinetic energy of the air within the chamber is negligible. Determine
the flowrate, Q, needed to support the vehicle. If the ground
clearance were reduced to 2 in., what flowrate would be needed? If
the vehicle weight were reduced to 5000 lb and the ground clearance
maintained at 3 in., what flowrate would be needed?
3.92 Water flows through a horizontal branching pipe as shown in
Fig. P3.92. Determine the pressure at section (3).
Skirt
Fan
Q
Vehicle
V 3
A 3 = 0.07 m 2 V 2
(2) p 2 = 350 kPa
A 2 = 0.02 m 2
(1)
V 1 = 4 m/s
p 1 = 400 kPa
A 1 = 0.1 m 2
F I G U R E P3.92
3.93 Water flows through the horizontal branching pipe shown in
Fig. P3.93 at a rate of 10 ft 3 s. If viscous effects are negligible, determine
the water speed at section 122, the pressure at section 132,
and the flowrate at section 142.
3.96 Water flows from the pipe shown in Fig. P3.96 as a free jet and
strikes a circular flat plate. The flow geometry shown is axisymmetrical.
Determine the flowrate and the manometer reading, H.
0.1-m
diameter
0.2 m
H
0.4 mm
V
(3)
F I G U R E P3.95
3 in.
A 2 = 0.07 ft 2
p 2 = 5.0 psi
0.01-m
diameter
(2)
Pipe
(1)
A 1 = 1 ft 2
Q 1 = 10 ft 3 /s
p 1 = 10 psi
F I G U R E P3.93
(4)
(3)
A 3 = 0.2 ft 2
V 3 = 20 ft/s
Q
F I G U R E P3.96
3.97 Air flows from a hole of diameter 0.03 m in a flat plate as
shown in Fig. P3.97. A circular disk of diameter D is placed a distance
h from the lower plate. The pressure in the tank is maintained
at 1 kPa. Determine the flowrate as a function of h if viscous