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The air also excerts pressure
on the surface of the liquid.
Hence, below the surface of the liquid
we have additional to the pressure of the air
the pressure of the weight of the liquid above each point.
The latter pressure grows with depth under the surface.
However, at each depth the total pressure on one side of the cylinder
is exactly cancelled by the total pressure on the opposite side.
Hence, also under the surface of the liquid,
one has that the pressure forces on the sides of the cylinder
have vanishing net result.
Consequently, we do not have to consider the effect
of the pressure on the sides of the cylinder,
neither above, nor below the surface of the liquid.
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