Deduce the pressure at a point inside a liquid at depth in upward direction?

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Solution

Fluid pressure is the pressure exerted by fluid(gas, liquid) at any point within that fluid.
There are certain conditions to satisfy first of all fluid should be incompressible and also it should be at rest.
Pressure within a liquid depends upon the density of the liquid, the acceleration due to gravity and the depth within the liquid.
4. Consider a liquid of density $ρ k g / m^{3}$ is filled in the vessel. Consider an imaginary cylinder PQRS, with height' $h$ ' and area of cross-section $A$ is in the liquid. such that the upper circular surface coincides with the surface of the water. The curved surface is surrounded by liquid and experiences equal and opposite thrusts on any horizontal line circularly parallel to its base. So it canceled the thrust on the curved vertical part of the cylinder.

Thrust on the lower part of the base will be due to the water column in the cylinder.
Weight or Thrust on circular surface, $F = m g$ $= A . h ρ g$
Pressure on surface SR= $\frac{F}{A}$ Therefore $P = \frac{A h ρ g}{A}$
Hence Pressure, $P = h ρ g$

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(e) Pressure of a liquid at a given depth is ___ to the density of liquid.

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