Deduce an expression for the pressure at a depth inside a liquid

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Solution

Consider a vessel containing a liquid with density $ρ$ .

Allow the liquid to be stationary

To calculate the pressure at a depth consider a horizontal circular surface PQ with area ; $A$ , depth $h$ below the free surface XY of the liquid
The pressure on surface PQ will be due to the weight of the liquid contained in cylinder PQRS of height h with PQ as its base and top face RS lying on the free surface XY of the liquids
Thrust exerted on the surface PQ

Volume of water column above the area PQ = $A * h$
Mass of the water column = $m = A h ρ$
weight of the water column = $m g = A h ρ g$

$p r e s s u r e = \frac{F o r c e}{A r e a}$
$p r e s s u r e = \frac{A h ρ g}{A}$
$p r e s s u r e = h ρ g$

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(b) Pressure is ___ in all directions about a point in a liquid.
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at a depth

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is :

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