Question

Derive an expression for Pressure due to the Liquid column.

Answer 1

A tall beaker filled with water to form a liquid column
Area of the cross-section at the bottom = A
Height of liquid column = h
The density of the liquid = ρ
Thrust at bottom of liquid column (F) = Weight of liquid.
F = mg …(1) (∵ m – mass of liquid)
Mass,m = ρ × V ……………… (2)
Volume of liquid columñ, V = Area of cross-section (A) × height (h)
V = Ah ………….(3)
Substitute (3) in (2) n, = ρ Ah ………………… (4)
Substitute (4) in (1) F = ρ Ahg ……………….(5)
Pressure (P) = 
∴ P = hpg – This is the expression for pressure due to the liquid column.