9702_s22_qp_12 Question 15

A closed U-shaped tube contains a stationary liquid of density ρ. One side of the tube contains a gas at pressure p₁ and the other side contains a gas at pressure p₂, as shown. 

The acceleration of free fall is g. Which equation is correct? 

A  p₁ = ρgy 

B  p₂ = ρg(x – z) 

C  p₁ – p₂ = ρg(y – z) 

D  p₁ + p₂ = ρgx

ANSWER: C

The Physics Behind

• Fluid pressure must be the same at same levels.
• At that level, that is, the surface of liquid at the left side of the U-shaped tube, the pressure is p₁.
• The pressure at the same level at the right side of tube is the combined pressure p₂ and the pressure due to the liquid above that liquid
• In equation form, the above gives

p₁ = p₂ + M

where M is the pressure due to the liquid above the level.

M = ρgh

where h is the length of the column of liquid above the level

Therefore,  p₁ = p₂ + ρgh

where h = y - z.