The pressure at the bottom face of a liquid is not affected by the shape of the container.

This is a stunning statement, but how do you prove it?

I am confused as the weight is not the same as that of a beaker containin water of the same height.

pressure is force per area, there is more force at the bottom, but there is also more area

take a conical flask, wide at the top and narrow at the botom, some of the downward force is taken by the sloping sides and isnt transfered to the narrow bottom.

 

it's easy to prove, get diffeent shaped flasks and a pressure meter.

actually, pressure can be measured in cm water, mercury, any liquid basically

where's the additional force from?

good question...

i think it's from the glass again, but down this time.

if you cut the flask across the middle, and managed to keep the water from spilling while allowing the top half to slide, the top half would actually move up, implying there's an upward force applied by the water.

since this force normally does no work, there *must* be an equal downward force applied by the glass

 

pressure is an omni-directional force, so the water at the top is applying pressure which is transfered outward without losing magnitude, (the glass serves to make this happen) so if the pressure doesnt lose magnitude, it will compound as you increase the head of water. (forgive the terminology)