First slide

Fluid statics

Question

A U–tube contains some non–viscous liquid upto a depth h. The tube starts moving to the right parallel to its base with constant acceleration ‘a’. Find the height of liquid column in arm(1)

Moderate

A

$(h + \frac{2 ab}{3 g})$
B

$(h + \frac{ab}{2 g})$
C

$(h + \frac{ab}{g})$
D

$(h + \frac{3 ab}{4 g})$

Solution

$tanθ = \frac{a}{g} \frac{h_{1} - h_{2}}{b} = \frac{a}{g}$
$\Rightarrow h_{1} - h_{2} = \frac{ab}{g} - - - (1) Also, (h_{1} + h_{2} + b) A = (h + h + b) A \Rightarrow h_{1} + h_{2} = 2 h - - - - (2) Solving, h_{1} = (h + \frac{ab}{2 g})$

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