fluid_mechanics

Problems 89
the tank has a specific weight of 27 kNm 3 . Determine the magnitude,
direction, and line of action of the force exerted on the curved
surface of the cone within the tank due to the 40-kPa pressure and
the liquid.
2.88 The homogeneous gate shown in Fig. P2.88 consists of one
quarter of a circular cylinder and is used to maintain a water depth
of 4 m. That is, when the water depth exceeds 4 m, the gate opens
slightly and lets the water flow under it. Determine the weight of
the gate per meter of length.
6 ft
Water
3 ft
Bulge
F I G U R E P2.92
Pivot
p A
4 m
Air
1 m
20 psi
4-ft diameter
5 ft
F I G U R E P2.88
2.89 The concrete 1specific weight 150 lbft 3 2 seawall of Fig.
P2.89 has a curved surface and restrains seawater at a depth of 24 ft.
The trace of the surface is a parabola as illustrated. Determine the
moment of the fluid force (per unit length) with respect to an axis
through the toe (point A).
Seawater
Water
F I G U R E P2.93
2 ft
Gage
fluid
(SG = 3.0)
2.94 A 3-m-diameter open cylindrical tank contains water and has a
hemispherical bottom as shown in Fig. P2.94. Determine the magnitude,
line of action, and direction of the force of the water on the
curved bottom.
2 ft
24 ft
y
y = 0.2x 2 15 ft
F I G U R E P2.89
A
x
8 m
Water
2.90 A cylindrical tank with its axis horizontal has a diameter of
2.0 m and a length of 4.0 m. The ends of the tank are vertical planes.
A vertical, 0.1-m-diameter pipe is connected to the top of the tank.
The tank and the pipe are filled with ethyl alcohol to a level of 1.5 m
above the top of the tank. Determine the resultant force of the
alcohol on one end of the tank and show where it acts.
2.91 If the tank ends in Problem 2.90 are hemispherical, what is
the magnitude of the resultant horizontal force of the alcohol on
one of the curved ends?
2.92 An open tank containing water has a bulge in its vertical side
that is semicircular in shape as shown in Fig. P2.92. Determine the
horizontal and vertical components of the force that the water exerts
on the bulge. Base your analysis on a 1-ft length of the bulge.
2.93 A closed tank is filled with water and has a 4-ft-diameter hemispherical
dome as shown in Fig. P2.93. A U-tube manometer is connected
to the tank. Determine the vertical force of the water on the
dome if the differential manometer reading is 7 ft and the air pressure
at the upper end of the manometer is 12.6 psi.
3 m
F I G U R E P2.94
2.95 Three gates of negligible weight are used to hold back water
in a channel of width b as shown in Fig. P2.95 on the next page. The
force of the gate against the block for gate (b) is R. Determine (in
terms of R) the force against the blocks for the other two gates.
Section 2.11 Buoyancy, Flotation, and Stability
2.96 Obtain a photograph/image of a situation in which
Archimedes’ principle is important. Print this photo and write a
brief paragraph that describes the situation involved.
2.97 A freshly cut log floats with one fourth of its volume protruding
above the water surface. Determine the specific weight of
the log.