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What is column pressure? Derive a relation for the same.

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Pressure exerted by a liquid due to its height is called column pressure.

Consider two points X and Y to be lying on the top and bottom circular faces of an imaginary cylinder of liquid. Let area of the circular faces by a each and height of the cylinder by h. If pressure exerted at point X is Px and at Y is Py, then

\(P_x=\frac{F_x}{a}\)

Fx = Pxa acting downward Weight of this cylinder, W = mg = Vρg = ahρg is also acting downwards so total downward force = Fx + W = Pxa + ahρg

The lower face of the cylinder experiences upward force given by

Fy = Pya.

In equilibrium, Fy = Fx + W

i.e., Pya = Pxa + ahρg

or (Px − Py) = hρg

or P = hρg

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