A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit?

Solution

Height of the spirit column, h₁ = 12.5 cm = 0.125 m
Height of the water column, h₂ = 10 cm = 0.1 m
P₀ = Atmospheric pressure,
ρ₁ = Density of spirit,
ρ₂ = Density of water,
Pressure at point B = P₀ + ρ₁h₁g
Pressure at point D = P₀ + ρ₂h₂g
Pressure at points B and D is the same.
P₀ + ρ₁h₁g = P₀ + ρ₂h₂g
ρ₁ / ρ₂ = h₂ / h₁
10 / 12.5 = 0.8
Therefore, the specific gravity of spirit is 0.8.