Question

Calculate the pressure due to water coloum height 100m when g is 10m/s2 and density of water 1000kg/m3​

Answer 1

Consider the water column having height h and cross sectional area A, so that the volume of the water column,

V = Ah

A = V / h

Let the water column have full of water of mass m. Then the force exerted on the water column by water is equal to the weight of the water, i.e.,

F = mg → (1)

But, the density of the water,

ρ = m / V

m = ρV

Then (1) becomes,

F = ρVg

Then, the pressure exerted by the water, known as hydrostatic pressure, is,

P = F / A

P = ρVg / (V / h)

P = ρVgh / V

P = ρgh

This is the expression for the hydrostatic pressure.

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So we are given,

h = 100 m

g = 10 m s^(-2)

ρ = 1,000 kg m^(-3)

Then, the pressure due to the water column is,

P = ρgh

P = 1,000 × 10 × 100 Pa

P = 10,00,000 Pa

or,

P = 1 MPa