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p - density of water, g - accel of gravity, h - dist below surface

And that this relationship holds regardless of the shape of the container of water. (also, I'm neglecting the atmospheric pressure at the surface)

If I have a cylindrical beaker of water of height H and area A and put it on a scale, I can calc the reading of the scale two ways...

1) pressure at bottom times area is pgHA.

2) density times volume times g is also pgHA.

Both ways give the same reading. Now if the shape of the beaker is an hourglass which has an area at top and bottom of A (same as top and bottom of cylindrical beaker), the two ways don't yield the same result.

Method 1) yields the same result for both shapes but method 2) yields a smaller result for the hourglass. What wrong with my logic? Thanks, Brett.