Question

A liquid column of 5 m and of density 500 kgm exerts a pressure of 25 k Pa at the bottom of a tank.
If another liquid of density 250 kgm-'is used instead, what should be the minimum height of the tank to get the same pressure at the bottom?​

Answer 1

Given: A liquid column of 5 m and of density 500 kg/cubic meter exerts a pressure of 25 k Pa at the bottom of a tank.

Density of liquid B is 250 kg/cubic meter.

To find: minimum height of the tank to get the same pressure at the bottom?

Step by step Explanation:

Pressure P at any point is given by the formula;

$P=D\times g\times h$

Where D is the density

g is acceleration due to gravity

h is the height

For pressure at bottom of tank to be equal:

$P_{1} = P_{2}\\D_{1}gh_{1} = D_{2} g h _{2}$

D1= density of liquid A= 500 kg/cubic m

h1= 5 m

D2= 250 kg/cubic m

on substituting the values in the equation, we get;

$500\times g\times 5= 250\times g\times h\\h=\frac{500\times 5}{250}\\h=10$

Hence the minimum height of the tank to get the same pressure at the bottom of tank is 10 meter.