Question

The hydrostatic pressure 'P' of a liquid column depends upon the density 'd' , height 'h' of liquid column and also an acceleration 'g; due to gravity. Using dimensional analysis, derive formula for pressure P.

Answer 1

It is given that the hydrostatic pressure is directly proportional to the following terms

$P=K{d}^x{h}^y{g}^z............\left(1\right)$

$K=cons\tan t$

Writing dimensional formula of pressure, density, height and acceleration due to gravity as

$\left[\frac{M}{L{T}^2}\right]={\left[\frac{M}{L^3}\right]}^x{\left[L\right]}^y{\left[\frac{L}{T^2}\right]}^z$

On comparing there powers, we get

$x=1$

$z=1$

$\&y=1$

Equation (1) becomes

$P=dgh$