O lvl Phy: Pressure

The figure below shows 3 liquids, liquid X, liquid Y and mercury, in a manometer. Given the information below, determine the density of liquid X and density of liquid Y.

Atmospheric pressure = 76 cm Hg
Density of mercury = 13600 k/m³
Density of liquid Y is twice of density of liquid X

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Answer:

We take the pressure of mercury by considering the red line as shown:

Let density of X be ρ_x, density of Y be ρ_y.

LHS: Pressure = atm + 0.05 ρ_x g + 0.02 ρ_mercury g
RHS: Pressure = atm + (0.16 - [0.08 - 0.02]) ρ_y g

Both sides pressure must be the same for mercury

atm + 0.05 ρ_x g + 0.02 ρ_mercury g = atm + 0.09 ρ_y g
0.05 ρ_x g + 0.02 ρ_mercury g = 0.10 ρ_y g

Because ρ_y= 2 ρ_x,
0.05 ρ_x g + 0.02 ρ_mercury g = 0.20 ρ_x g
0.05 ρ_x + 0.02 ρ_mercury = 0.20 ρ_x
0.02 ρ_mercury = 0.15 ρ_x
ρ_x = 0.02 / 0.15 * ρ_mercury
ρ_x = 1813 kg/m³

Thus, ρ_y = 2 ρ_x = 3627 kg/m³

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