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Question

Water stands upto a height h behind the vertical wall of a dam. What is the net horizontal force pushing the dam down the stream, if width of the dam is σ? (ρ= density of water)

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Solution

Let, an an infinitesimal dy change in h

And the gauge pressure at a dept y from the surface of the dam is

p=pgy

Here, density of water is p and the acceleration due to gravity is g

The resultant force on the wall is

F=pdxy .........(1)

F=pdydx

We already know that dx=σ

Now substituting pgy for p and σ for dx in equation (1)

F=pdydx=ydyσ=pgσh0ydy=pgσy220hF=pgσh22


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