11/10/2025
PRESSURE IN SOLIDS AND FLUIDS
Pressure is defined as the perpendicular force per unit area acting on a surface.
Symbolically we can write:
P = F/ A
Where:
F is the force in Newton(N)
A is the area in m^2
P is the pressure in N/m2 or Pascal(Pa)
PROBLEM
Q1. Calculate the pressure exerted on the ground by a person weighing 70kg whose two feet cover an area of 400cm2. If the man stands on one foot, what is the new pressure he exerts on the ground?
Solution ⭐
P = F/A
Force due to the weight of the person is given by:
F = mg
= 70 × 10 ( since g = 10m/s^2
= 700N.
Area covered by the two feet = 400 cm^2
Or 400/100×100 = 0.04m^2
P = F / A = 700/0.04
= 17.5 × 10^3 N/m2
If the person stands on one foot, area is halved , i.e.
A = 0.02
P = 700/0.02
= 35 × 10^3 Nm^2
Thus the pressure is twice as much.
PRESSURE IN FLUID
Unlike solids which exert pressure only downwards, liquid exert pressure in all directions. Other important characteristics of liquid pressure are:
• the pressure at all points at the same level within a liquid is the same.
• the pressure in a liquid increases in direct proportion to the depth of the liquid.
• the pressure in different liquids at the same depth varies directly with density.
CAUSES OF PRESSURE IN FLUID
➡️Liquids:
•Pressure in liquids is primarily due to gravity.
The weight of the liquid column above a certain point creates the pressure.
•Pressure increases with the depth of the liquid, as there is more fluid weight above.
•Denser liquids exert more pressure at the same depth compared to less dense fluids.
Without gravity, a liquid would not
➡️Gases:
Pressure in gases is caused by the continuous random motion of gas molecules.
• These molecules collide with each other and the walls of the container, resulting in pressure.
• Temperature significantly influences gas pressure; higher temperatures lead to more frequent and energetic collisions, increasing pressure.
FORMULA FOR PRESSURE IN FLUIDS
Consider a liquid of density ρ in a cylinder of depth h, and area A
Then,
Volume of liquid (V) = A × h = Ah
Mass of liquid = V x ρ (V = Ah)
= Ahρ
Weight of liquid = Ahρg
Pressure, P = F/ A = Ahρg/A
= hρg
P = hρg
Where:
P is the pressure
h is the depth or height of the liquid
ρ (rho) is the density of the fluid
g is the gravitational acceleration
GENERAL FACTORS AFFECTING PRESSURE
1. Force:
A greater force applied to a surface results in higher pressure.
2. Surface Area:
The same force applied over a smaller area creates more pressure than when applied over a larger area.
3. Depth:
In fluids, pressure increases with depth because of the weight of the fluid above.
