Question
Find an expression for pressure at a depth h inside a liquid of density d.
Answer
Consider a vessel containing a liquid of density ρ. Let the liquid be stationary. In order to calculate the pressure at a depth, consider a horizontal circular surface PQ of area A at a depth h below the free surface XY of the liquid. The pressure on the surface PQ will be due to the thrust of the liquid contained in cylinder PQRS of height h with PQ as its base and top face RS lying on the free surface XY of the liquid.
Total thrust exerted on the surface PQ
= Weight of the liquid column PQRS
= Volume of liquid column PQRS × density × g
= (Area of base PQ × height) × density × g
= (A × h) × ρ × g
This thrust is exerted on the surface PQ of area A. Therefore, pressure is given as shown below.
P = {Ahρg\over A} = hρgThus, Pressure = depth × density of liquid x acceleration due to gravity.
