Physics

# 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.

##### SOLUTION

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

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

$K=cons\tan t$

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

$x=1$

$z=1$

$\And \,\,y=\,1$

Equation (1) becomes

$P=dgh$

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Subjective Medium Published on 18th 08, 2020
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