Thrust: The net force exerted by a liquid on any shield in contact with it, is known as thrust of liquid.
Pressure: The thrust operated by a liquid per unit area of the field in contact with the liquid is known as pressure.
If F is the thrust operated by a liquid on a surface of area A, Then pressure is shown by, P=F/A
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The unit of pressure is dyne N m-2 in SI and cm-2 in cgs system. A pressure of 1 N m-2 is also named as 1 pascal (Pa).
1 Pa (or 1 N m-2) = 10 dyne cm-2
The dimensional relation of pressure is [M L-1 T-2].
Derivation of pressure at any position in a fluid
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Let PA be the atmospheric pressure over the free surface of the liquid. Now let us take an imaginary cylindrical volume under the liquid. It is in equilibrium because we are operating with the hydrostatics. Our liquid is not compressible so.
P0 A + mg - PA = 0 or PA - P0A = ρg (y0 -y)A
=> P = P0 + ρg (y0 - y) => dP/dy = - Pg ... (i)
and if y0 = 0 & y = -h & P0 = PA
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P = PA + Pgh ... (ii)
=> If dy < 0 dp > 0 & dy < 0 dp < 0
Increase height gives drop in pressure and decreasing height means increase in pressure.
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