A manometer (shown below) that is open to the atmosphere contains mercury (SG = 13.6) with a layer of oil floating on the mercury in the right leg. If the level of the mercury in the left leg is 2 cm above the mercury level in the right leg, and the oil layer on the right is 8 cm above the mercury level in the right leg. What is the density of the oil?

3400 kg/m³

Explanation:

Given:

Specific gravity of the mercury = 13.6

therefore, the density of mercury = 13.6 * 1000 = 13600 kg/m³

Level of mercury in the left limb = 2 cm above the mercury level in right limb

= 0.02 m

Level of oil layer in the right limb = 8 cm above the mercury level in right limb

0.08 m

Now,

Pressure in manometer is given as = ρgh

where,

ρ is the density

g is the acceleration due to gravity

h is the height of the liquid above datum

also,

pressure in right limb = pressure in the left limb (for the equilibrium)

thus,

ρ₁gh₁ = ρ₂gh₂

here,

ρ₁ = density of oil

ρ₁ * g * 0.08 = 13600 * g * 0.02

or

ρ₁ = 3400 kg/m³