Mechanics | Relativity Answers

A long solid cylinder of radius 0.8 m hinged
at point A is used as an automatic gate, as
shown in Fig. beside. When the water level
reaches 5 m, the gate opens by turning about
the hinge at point A. Determine (a) the
hydrostatic force acting on the cylinder and
its line of action when the gate opens and (b)
the weight of the cylinder per m length of the
cylinder

Consider a 1.73-m-tall man standing vertically in water and
completely submerged in a pool. Determine the difference between
the pressures acting at the head and at the toes of this man, in kPa.

A crane is used to lower weights into
the sea (density 1025 kg/m3
) for an
underwater construction project (Fig.
below). Determine the tension in the
rope of the crane due to a rectangular
0.4-m x 0.4-m x 3-m concrete block
(density 2300 kg/m3
) when it is (a)
suspended in the air and (b) completely
immersed in water

A long solid cylinder of radius 0.8 m hinged at point A is used as an
automatic gate, as shown in the Fig below. When the water level
reaches 5 m, the gate opens by turning about the hinge at point A.
Determine (a) the hydrostatic force acting on the cylinder and its
line of action when the gate opens and (b) the weight of the cylinder
per m length of the cylinder?

A heavy car plunges into a lake during an accident and lands at the
bottom of the lake on its wheels as shown in the Fig below. The
door is 1.2m high and 1m wide, and the top edge of the door is 8m
below the free surface of the water. Determine the hydrostatic force
on the door and the location of the pressure center, and discuss if
the driver can open the door?

1. Define the resultant hydrostatic force acting on a submerged surface,
and the center of pressure.
2. You may have noticed that dams are much thicker at the bottom.
Explain why dams are built in this way.
3. Consider a submerged curved surface. Explain how you would
determine the horizontal component of the hydrostatic force acting on
this surface.
4. Consider a submerged curved surface. Explain how you would
determine the vertical component of the hydrostatic force acting on this
surface.
5. Consider a circular surface subjected to hydrostatic forces by a constant
density liquid. If the magnitudes of the horizontal and vertical
components of the resultant hydrostatic force are determined, explain
how you would find the line of action of this force?

The water in a tank is pressurized by air,
and the pressure is measured by a multifluid manometer as shown in the Fig. The
tank is located on a mountain at an
altitude of 1400 m where the atmospheric
pressure is 85.6 kPa. Determine the air
pressure in the tank if ℎ1 = 0.1 m, ℎ2 =
0.2 m, and ℎ3 = 0.35 m. Take the
densities of water, oil, and mercury to be
1000 kg/m3
, 850 kg/m3
, and 13,600
kg/m3
, respectively?

A manometer is used to measure the
pressure in a tank. The fluid used has a
specific gravity of 0.85, and the
manometer column height is 55 cm, as
shown in the Fig. If the local atmospheric
pressure is 96 kPa, determine the
absolute pressure within the tank?

1. Explain why some people experience nose bleeding and some others
experience shortness of breath at high elevations.
2. Someone claims that the absolute pressure in a liquid of constant
density doubles when the depth is doubled. Do you agree? Explain.
3. A tiny steel cube is suspended in water by a string. If the lengths of
the sides of the cube are very small, how would you compare the
magnitudes of the pressures on the top, bottom, and sides of the
cube?
4. Express Pascal’s law, and give a real world example of it.
5. Consider two identical fans, one at sea level and the other on top of
a high mountain, running at identical speeds. How would you
compare (a) the volume flow rates and (b) the mass flow rates of
these two fans?
6. The diameters of ram and plunger of an hydraulic jack press 200
mm and 30 mm respectively. Find the weight lifted by the hydraulic
press when the force of applied at the plunger is 400 N?

A plate having an area of 0.6 m2
is sliding down an inclined plane
at 30° to the horizontal with a velocity of 0.36 m/s. There is a
cushion of fluid 1.8mm thick between the plane and the plate. Find
the viscosity of the fluid if the weight of the plate is 280N?