Question

Find the density of a liquid, in lb/ft^3, that exerts a pressure of 0.400 lb/in^2 at a depth of 42.0 in.

Answer 1

Given :

Pressure, P = 0.4 lb/in².

Depth, h = 42 in.

To Find :

The density of a liquid.

Solution :

Pressure at height h of a liquid of density $\rho$ is given by :

$P = \rho g h$   ....1)

Here, g = 386.04 in/s²( acceleration due to gravity )

Putting all values in equation 1, we get :

$P = \rho g h\\\\0.4 = \rho\times 386.04 \times 42\\\\\rho=\dfrac{0.4}{42\times 386.04}\ lb/in^3\\\\\rho=\dfrac{0.4}{42\times 386.04}\times 12^3\ lb/ft^3\\\\\rho=0.0426\ lb/ft^3$

Hence, this is the required solution.