First slide

Fluid statics

Question

Three immiscible and non-reacting liquids of densities P, 2P and P/2 are in a U-tube as shown in the figure. Free surfaces of liquids in the two arms of the U-tube are in the same horizontal level. Then the length ‘x’ of the liquid column of density $\frac{P}{2}$ is [l = 27 cm]

Moderate

A

6 cm
B

12 cm
C

18 cm
D

9 cm

Solution

Equating pressures at points A and B, we can write
$ρ . g . l = \frac{ρ}{2} . g . x + 2 ρ . g . (l - x)$
$\begin{array}{l} \Rightarrow l = \frac{x}{2} + 2 l - 2 x \\ \Rightarrow x = \frac{2 l}{3} = \frac{2 \times 27}{3} cm = 18 cm \end{array}$

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