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Air or water pressure can be calculated by the volume of air (or water) column and density. The column volume is usually calculated as the base area times the height. However since on a spherical earth, weight is directed towards the center of the earth, it should be more accurate to think of the column shape as a conical frustum, where the base is slightly smaller in area compared to the top.

Practically, probably the difference between this and say a cylinder is negligible. Theoretically it exist, but I couldn't find any mention of it. Am I missing a certain keyword or a terminology? Or simply a case of "We don't care" ?

Bashar Gharaibeh
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In the standard explanation using a cylinder, we can calculate the pressure by first dividing the cylinder in small slices. For each slice the total force on the slice should be zero in equilibrium:

$p_{bottom}*A_{bottom} - p_{top} * A_{top} - A \rho * g * h = 0$,

where $p$ is pressure, $A$ the surface area, $rho$ the density, $g$ acceleration and $h$ the height of the slice. Then, if one knows the pressure difference per slice, one can calculate the total pressure.

One important property of the cylinder is that the top and bottom surface of each slice have the same size. Another important property of the cylinder is that the sides are parallel. This means that any forces on one side of the cylinder will be canceled by forces on the other side.

Your intuition is based on the fact that for slices of a cone, the top and bottom surface are not equal. This leads you to think that this means that therefore the pressure increase per slice should be higher than for the cylinder.

However, you do not take into account that for a cone, the sides are not parallel. Therefore, the forces on the sides of the cone do not cancel. The cone is effectively pushed up by the surrounding air pressure. This effect exactly cancels the effect of the bottom area being smaller than the top area.

Crimson
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In a liquid, the depth is not likely to be large enough for the difference between calculated pressure and measured pressure to be noticeable. In the atmosphere, variations in density due to altitude and temperature would likely mask any such effect.

R.W. Bird
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