Question

The equation determining the liquid pressure in a tank is z = P/rg where z is the depth, P is the pressure, r is the density and g is the acceleration due to gravity. Show that the two sides of the equation are dimensionally the same.

Answer 1

Consider the equation:

$$z = P/rg.$$

Let us show that

$$\frac{P}{\rho g}=[\text{m}].$$

Remember that pressure is

$$P=[\text{N/m}^2]=[\text{kg m/(m s)}^2],\\ \rho=[\text{kg/m}^3],\\ g=[\text{m/s}^2].$$

Substitute these values:

$$\frac{P}{\rho g}=\frac{[\text{kg}][\text{m}][\text{m}^3][\text{s}]^2}{[\text{m}^2][\text{s}^2][\text{kg}][\text{m}]}=[\text{m}].$$