First slide

Fluid statics

Question

Two identical cylindrical vessels with their bases at same level each contains a liquid of density d. The height of the liquid in one vessel in h₁, and that in the other vessel is h₂. The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected is

Moderate

A

$(h_{1} - h_{2}) gd$
B

$(h_{1} - h_{2}) gAd$
C

$\frac{1}{2} {(h_{1} - h_{2})}^{2} gAd$
D

$\frac{1}{4} {(h_{1} - h_{2})}^{2} gAd$

Solution

see fig
Work done = Initial potential energy - final potential energy
$= \frac{Adg}{2} [h_{1}^{2} + h_{2}^{2} - {(\frac{h_{1} + h_{2}}{2})}^{2}] = \frac{Adg}{4} {(h_{1} - h_{2})}^{2}$

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