A liquid of density ρ is filled in a U-tube is accelerated with an acceleration a so that the height of liquid in its two vertical arms are h 1 and h 2 as shown in the figure. If l is the length of ho

Question

A liquid of density ρ is filled in a U-tube is accelerated with an acceleration a so that the height of liquid in its two vertical arms are h 1 and h 2 as shown in the figure. If l is the length of horizontal arm of the tube, the acceleration a is

TestHub · Accepted Answer

Pressure on left end of horizontal tube,

$p_{1} = p_{0} + h_{1} ρ g$

Pressure on right end of horizontal tube,

$p_{2} = p_{0} + h_{2} ρ g$

As $p_{1} > p_{2}$ , so acceleration should be towards right hand side. If $A$ is the area of cross-section of the tube in the horizontal portion of U-tube, then

$p_{1} A - p_{2} A = (l A ρ) a$

Or $(h_{1} - h_{2}) ρ g A = l A ρ a$

$a = g \frac{(h_{1} - h_{2})}{l}$

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