Pressure in Liquids

Definition:

Pressure in liquids is the force exerted by the liquid per unit area. This pressure increases with depth due to the weight of the liquid above.

Formula:

 P=ρgh

• P is the pressure.
• ρ (rho) is the density of the liquid (how heavy the liquid is per unit volume).
• g is the acceleration due to gravity (approximately 9.8 m/s2 on Earth).
• h is the height or depth of the liquid column above the point where you’re measuring the pressure.

Derivation of the Pressure in Liquids Formula

Concept: Pressure in a liquid at a certain depth is due to the weight of the liquid above that point.

Steps to Derive the Formula

1. Consider a Column of Liquid: 

Imagine a vertical column of liquid with height h, cross-sectional area A, and density ρrhoρ.

2. Weight of the Liquid Column: The weight (W) of the liquid column can be calculated using: W=mass×g

Where g is the acceleration due to gravity.

3. Mass of the Liquid: The mass (m) of the liquid in the column is: m=ρ×V

Where V is the volume of the liquid. 

For a column of height h and cross-sectional area A: 

V=A×h 

So, m=ρ×(A×h)

m=ρAh

4. Weight of the Liquid: 

Substituting the mass into the weight equation: 

W= m × g   but   m=ρAh

So, W=(ρAh)×g

5. Pressure is Force per Unit Area: 

Pressure (P) at the bottom of the column is the force exerted by the weight of the liquid divided by the area: 

P=W/A

Substituting the weight: 

P=ρAhg / A

P=ρhg

•  Pressure Increases with Depth: The deeper you go in a liquid, the greater the pressure because there’s more liquid above you pushing down.
• Pressure is Equal in All Directions: At any given depth, the pressure in a liquid is the same in all directions.