Question

Derive an expression for liquid pressure at a point inside the liquid

Answer 1

Answer:

Force in a fluid = Thrust= weight of the liquid = (volume of liquid × density × Acceleration due to gravity.) However when the liquid is exposed to the atmosphere, you have to factor in the pressure due to the column of the air....

Answer 2

Liquid Pressure ( P ) = hρg

Let us consider a horizontal area 'A' of a container having a the point 'P' at a depth of 'h' below the surface of the liquid whose density is 'ρ'.

Imagining a vertical column inside the liquid with a base whose area is 'A'.

Thus, volume of the liquid column will be = A×h

As the vertical column is in a shape of a cylindrical, therefore volume = πr2h, (Volume of a cylinder)

where πr2 = A[area of the cylindrical base]

and h = height

Mass of the liquid column = volume×density

= (A×h)×ρ

Also we know,

F = m×g

= (A×h×ρ)×g

Pressure (P)

= Force (F) / Area (A)

= (A×h×ρ×g) / A

P = hρg

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