Pressure in fluids and atmospheric pressure
numericals
1. Calculate the pressure exerted by 0.8m vertical length of alcohol of density 0.8g /cm3 in
pascal.
2. The base of a cylindrical vessel measures 300 cm2 water is poured into it to a depth of 6
cm.
3. Normal pressure of air is 76cm of mercury. Calculate its pressure in SI units. Ρhg = 13600
kg/m3, g = 10m/s2.
4. The pressure of water on the ground floor is 1, 60, 000 Pa. calculate the pressure on the
5th floor at a height of 15m.
5. The atmospheric pressure at a place is 650mm of mercury. Express the pressure in Pascal
and millibar. Given that density of mercury is 13600 kg.
6. A cube of each side 5 cm is placed inside a liquid. The pressure at the centre of one face of
cube is 10 Pa. calculate the thrust exerted by the liquid on this face.
7. Pressure at the bottom of the sea is 8, 968, 960 Pa. if the density of water is 1040 kg/ m3.
Calculate the depth of sea.
8. The atmospheric pressure is 105 N/m2 and density of water is 103kg/m3. Calculate the
depth of water at which pressure is double the atmospheric pressure.
9. Atmospheric pressure at sea level is 76 cm of Hg. Calculate the vertical height of air
column exerting the above pressure. Assume the density of air is 1.29 kg/m3 and that of
Hg = 13600 kg/m3. Why is the height calculated by you far less than the height of
atmosphere?
10.The pressure of water on the ground floor is 1, 50, 000 Pa whereas pressure on the 4th
floor is 30,000 Pa. calculate the height of the four floors.
11.A metal plate of length 1.5m and width 0.2 m is placed 40cm below alcohol of density 800
kg/m3, the atmospheric pressure is 80cm of Hg. Calculate force experienced by the plate.
(give density of mercury = 13600 kg/m3.)
12.In a hydraulic machine, two pistons are of cross section in the ratio 2:10. What force is
needed on the narrow piston to overcome a force of magnitude 200N on wider piston?
13.A barometer with mercury reads 75cm, when 3 cm3 of atmospheric air is introduced into
the tube, the mercury suddenly falls to a height of 65cm and the air column length above
the mercury is obtained to be 15cm, what is the cross sectional area of the barometer
tube?
14.A cube of each side 15cm is immersed in a tube containing water of density 103 kg/m3
such that its top surface is 20cm below the free surface of water. Calculate
1. Pressure at the top of the cube
2. Pressure at the bottom of the cube
(atmospheric pressure = 105Pa and g = 9.8 m/s2.)
15.An air bubble rises from the bottom of a lake of depth 10.34m to its surface. Compare the
pressure on bubble at the bottom to that on the surface. (atmospheric pressure = 0.76 m
of Hg, density of Hg= 13.6 X 103 kg/m3, density of water = 103 kg/m3)
Pressure in fluids and atmospheric pressure
numericals
16.What is the depth below the surface of water with pressure being equal to twice the
atmospheric pressure? Here the atmospheric pressure is 20 N/cm2, density of water is 103
kg/m3 and g = 9.8 m/s2.
17.A U tube is first partly filled with mercury. Then water is being added in one arm and oil in
the other arm. Find the ratio of water and oil columns so that mercury level is same in
both the arms of U tube. Given density of oil = 900 kg/m3.
18. The area of cross – section of press plunger of a hydraulic press is 8m2. A resistive load of
400kgf must be surmounted on it. Evaluate the required force on the pump plunger if
area of cross – section is 0.05m2.
19.A vessel of base area 100cm X 60 cm and height 200cm is totally filled with a liquid of
density 1. 1 X103 kg/m3. Ignoring the atmospheric pressure, calculate :
a. The thrust of the vessel at the bottom
b. The pressure of the vessel
c. The pressure at the depth of 5cm from the surface
d. The net force experienced by a metal foil of area 10 cm2 which is placed at a depth of
5cm from the free surface.