- #1

Jahnavi

- 848

- 102

## Homework Statement

Prove that the hydrostatic pressure difference between the liquid surface and the base of

**rightmost tube**is ρgh (h is the vertical distance of the liquid surface from the base ) ?

## Homework Equations

## The Attempt at a Solution

I would like to prove this result just out of curiosity .

The tube is tilted at an angle θ with the vertical . Tube length is L .

Consider a small cuboidal shape fluid element of base area A and height dx at a distance x from the base of the tube .

Weight of the fluid element = (Adx)ρg

Since the fluid is in equilibrium , the net force along the length of the tube is zero .

If P (x) denotes pressure at a distance x from the base ,

P(x)A - P(x+dx)A - (Adx)ρg(cosθ) = 0

dP = ρg(cosθ)dx

P(0) - P(L) = ∫ ρg(cosθ)dx

= ρgL(cosθ)

= ρgh

Is this derivation correct ?