Question

Derive pressure at a point inside a liquid at rest. (Establish the relation P = dhg)​

Answer 1

Explanation:

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Answer 2

P = dhg is a formula which is used for calculating the pressure exerted by any liquid at a certain depth.

Derivation of pressure at a point inside a liquid at rest.

Let a vessel with a cross-sectional area be 'A' filled with any liquid of density be 'd', volume be 'V' and mass be 'm' up to the height be 'h'. Now, ‘h’ is termed to be the depth of liquid from the free surface.

According to the definition of Pressure,

P = F/A

As we know, F = mg

P = mg/A

As we know, m = Vd

P = Vdg/A

As we know, V = Ah

P = Ahdg/A

By reducing A from both the numerator and denominator

P = dhg ( g is the acceleration due to the gravity of that place)

Hence, P = dhg

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