Pressure in fluids is a key concept in physics and fluid mechanics. Fluids—liquids and gases—exert pressure in all directions due to the random motion of their particles. This concept helps explain natural phenomena and is widely applied in devices like barometers, hydraulic systems, and fluid pipelines.Important topics include types of pressure, pressure at depth, the hydrostatic paradox, and tools such as the barometer and U-tube manometer—all vital for exam preparation and understanding fluid behavior in static and dynamic conditions.
Pressure (P) is defined as the amount of normal force applied per unit area of surface.
here F⊥ = normal force on a surface of area A
760 mm of Hg=10.33 of water
; 1 torr=1 mm of mercury column=133 Pa
Pressure is of three types
Note: Barometer is used to measure the atmospheric pressure.
Note: Gauge pressure is always measured with the help of a "manometer".
When a liquid is at rest, it exerts pressure on the walls and base of its container. This pressure escalates with depth due to the weight of the liquid above.
m = mass of liquid element
A = Area of cross - section of liquid element
Since fluid is at rest,
Note: Pressure exerted by the same liquid at any point does not depend on the shape and size of the container (it means quantity of liquid). It depends only on the height of the liquid column.
The Hydrostatic Paradox refers to the observation that the pressure at a given depth in a fluid is the same, regardless of the shape or size of the container holding the fluid.
Pressure due to liquid,
Pressure due to liquid on a vertical wall is different at different depths, so average fluid pressure on side wall of the container is equal to mean pressure
(h = height of wall)
Working:
Standard atmospheric pressure = 76 cm (760 mm) of Hg at sea level
Atmospheric Pressure
Barometer in lift
Case (1) : Lift accelerating upwards with acceleration 'a'
Case (2) : Lift accelerating downwards with acceleration 'a'
U-Tube Manometer
For the same stationary liquid, pressure at the same horizontal level remains the same.
Illustration-1: An open U-tube contains water and unknown liquid separated by mercury. The mercury columns in two arms are level with 8 cm of water in one arm and 10 cm of unknown liquid in the other. Find the specific gravity of unknown liquid.
Solution:
Illustration-2: A cuboid (a × a × 2a) is filled with a liquid of density '' as shown in figure. Neglecting atmospheric pressure, find out (a) Force on base wall of the cuboid (b) Force on side wall of the cuboid.
Solution:
(a) Force on base wall=
(b) Force on side wall=
Illustration-3. A vertical tank is 5 meters tall. It is first filled halfway with water, and then the remaining half is filled with oil having a density of 0.85 g/cm³. What is the total pressure exerted by the liquids at the bottom of the tank?
Solution:
Pressure at the bottom,
Illustration-4. A girl weighing 50 kg stands balanced on a single high-heeled shoe. The heel has a circular base with a diameter of 1 cm. Calculate the pressure exerted by the heel on the floor. g=10 m/s2
Solution:
Pressure delivered by the heel on the horizontal floor is
(Session 2025 - 26)