The U tube in the figure contains two liquids in static equilibrium. The water of density ρ_w (1000 kg/m³) is in the right arm and oil of unknown density ρ_x is in the left arm. If l = 80 mm and d = 20 mm, then the density ρ_x of the oil is

Concept:

In an open tube manometer

• The pressure at both the open ends is atmospheric.
• The pressure at any point inside the column can be calculated from either side.

Calculation:

Given:

ρ_water = 1000 kg/m3, l = 80 mm and d = 20 mm

So, the pressure at the bottom of the oil column can be equated from either end to find the required value of ρ_oil.

ρ_oil × g × (d + l) = ρ_water × g × l

ρ_oil × (20 + 80) = 1000 × 80

ρ_oil = 800 kg/m3

Hence the required density of oil is 800 kg/m3.