Question

A column of oil of height 70.0 cm supports a column of an unknown liquid as suggested in the figure (not drawn to scale). Assume that both liquids are at rest and that the density of oil is 840 kg/m³. Determine the density of the unknown liquid.

Answer 1

Given

Height of the oil coloumn, h1 = 0.7 m

Density of oil, ρ1 = 840 kg/m^3

Height of the unknown liquid coloums, h2 = 0.27 m

The pressure is the atmospheric pressure, P1 = P2 = 1 atm

Since, the liquids are at rest, velocities v1 = v2 = 0 m/s

Using Bernoulli's equation

P1 + 1/2 ρ1 v1^2 + ρ1 g y1 = P2 + 1/2 ρ2 v2^2 + ρ2 g y2

1 atm + 0 + (840 kg/m^3) (9.8 m/s^2) (0.7 m) = 1 atm + 0 +  ρ2  (9.8 m/s^2) (0.27 m)

ρ2 = 2177.78 kg/m^3 is the density of unknown liquid