Question

A fluid, of density p, is at rest in acontainer, if the pressure at top of the container is P0, find an expression for the pressure at a point located at vertical depth h below the top of container..

Spammers stay away!
BrainlyStars account :)​

Answer 1

Answer:

P0-hpg

Explanation:

Let height of container = H

Pressure at top = Hpg = P0

Pressure at a depth "h" below the top = (H-h)pg

                                                               = Hpg-hpg

                                                                = P0-hpg

Answer 2

Answer:-  p = p₀ + hρg

Explanation:-

Let us take the container which is filled with fluid which is equilibrium.

Let us consider there are two points A and B  at a vertical distance of h. Now imagine a cylindrical column whose cross section area is 'A' and and C and D are its extremum points vertically as shown in the figure.

if the weight of  the water inside is m then,

weight of this imaginary cylinder will be = mg

= Volume × Density × g

= Ah × ρ × g

= Ahρg

This force works vertically downward.

Let the pressure a A and B be  p₁ and p₂ respectively.

Force at face A will be p₁  which is vertically downward and force at face B will be  p₂ which is vertically upward.

Since the system is under equilibrium thus,

(p₁A + mg) - p₂A = 0

p₁A + Ahρg - p₂A = 0

(p₂ - p₁)A = Ahρg

(p₂ - p₁) = hρg

Thus it is obvious that pressure given by  a fluid at height h is,

p' = hρg

Since it is already given that pressure at top of container is p₀ thus

Total Pressure = p₀ + hρg

p = p₀ + hρg