Question

You come across an open container that is filled with two liquids. Since the two liquids have different densities, there is a distinct separation between them. Water, which has a density of ρw=1.00×103 kg/m3, fills the lower portion of the container to a depth of 0.215 m. The fluid that is floating on top of the water is 0.342 m deep. If the absolute pressure on the bottom of the container is 1.049×105 Pa, what is the density, ρl, of the unknown fluid? The acceleration due to gravity is g=9.81 m/s2 and atmospheric pressure is P0=1.013×105 Pa.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = $\rho$_w = 1000 kg/m³

Density of the unknown liquid = $\rho$_l

Atmospheric pressure = P_atm = 1.013 x 10⁵ Pa

Height of the water in the container = H_w = 0.215 m

Height of the unknown liquid = H_l = 0.342 m

Absolute pressure at the bottom of the container = P = 1.049 x 10⁵ Pa

P = P_atm + $\rho$_wH_wg + $\rho$_lH_lg

1.049x10⁵ = 1.013x10⁵ + (1000)(0.215)(9.81) + $\rho$_l(0.342)(9.81)

$\rho$_l = 444.36 kg/m³

Density of the unknown fluid = 444.36 kg/m³