Mechanics of Fluids

2.18 In the vertical end of an oil tank is a plane rectangular inspection
door 600 mm wide and 400 mm deep which closely fits an
aperture of the same size. The door can open about one vertical
edge by means of two hinges, respectively 125 mm above
and below the horizontal centre-line, and at the centre of the
opposite vertical edge is a locking lever. Determine the forces
exerted on each hinge and on the locking lever when the tank
contains an oil of relative density 0.9 to a depth of 1m above
the centre of the door and the air above the oil surface is at
a gauge pressure of 15 kPa.
2.19 A vessel of water of total mass 5 kg stands on a parcel balance.
An iron block of mass 2.7 kg and relative density 7.5 is suspended
by a fine wire from a spring balance and is lowered into the
water until it is completely immersed. What are the readings on
the two balances?
2.20 A cylindrical tank of diameter 3d contains water in which a
solid circular cylinder of length l and diameter d floats with its
axis vertical. Oil is poured into the tank so that the length of
the float finally protruding above the oil surface is l/20. What
vertical movement of the float has taken place? (Relative density
of oil 0.8, of cylinder 0.9.)
2.21 A hollow cylinder with closed ends is 300 mm diameter and
450 mm high, has a mass of 27 kg and has a small hole in the
base. It is lowered into water so that its axis remains vertical.
Calculate the depth to which it will sink, the height to which
the water will rise inside it and the air pressure inside it. Disregard
the effect of the thickness of the walls but assume that
it is uniform and that the compression of the air is isothermal.
(Atmospheric pressure = 101.3 kPa.)
2.22 A spherical, helium-filled balloon of diameter 800 mm is to
be used to carry meteorological instruments to a height of
6000 m above sea level. The instruments have a mass of
60 g and negligible volume, and the balloon itself has a
mass of 100 g. Assuming that the balloon does not expand
and that atmospheric temperature decreases with increasing
altitude at a uniform rate of 0.0065 K · m −1 , determine the
mass of helium required. Atmospheric pressure and temperature
at sea level are 15 ◦ C and 101 kPa respectively; for air,
R = 287 J · kg −1 · K −1 .
2.23 A uniform wooden cylinder has a relative density of 0.6.
Determine the ratio of diameter to length so that it will just
float upright in water.
2.24 A rectangular pontoon 6mby3minplan, floating in water,
has a uniform depth of immersion of 900 mm and is subjected
to a torque of 7600 N · m about the longitudinal axis. If the
centre of gravity is 700 mm up from the bottom, estimate the
angle of heel.
Problems 87