Question

A certain liquid has a unit weight of 57 KN/m^3. Compute the mass density in kg/m^3.

Answer 1

A unit weight is

$\displaystyle \gamma =\frac{P}{V} =57 \cdot 10^3\; \frac{N}{m^3}$

By definition, weight $P = mg \Rightarrow m = \displaystyle \frac{P}{g}$

Mass density is

$\displaystyle \rho = \frac{m}{V} = \frac{P}{gV} = \frac{P}{V} \cdot \frac{1}{g} = \frac{\gamma}{g} = \frac{57 \cdot 10^3}{9.81} = 5.81 \cdot 10^3 \; \frac{kg}{m^3}$

Answer: $5.81 \cdot 10^3 \; \frac{kg}{m^3}$.