Why is pressure $rho g R$ at all points on the base of this upside-down container

Question

The container is inverted and filled with water through a hole on top and it is said the pressure on the bottom of the container is $rho g R $ which I agree with for only the point directly bellow the hole
I suppose the normal forces from the walls of the container would have an effect but why does it have to be such that the bottom gets exactly  $rho g R $. In the whole scenario atmospheric pressure is not present.

Adrian Howard · Accepted Answer

Water pressure increases with depth. All across the same horizontal depth the pressure is the same, ignoring the negligible curvature of the Earth. If the container is filled all of the way up to the hole as stated then the depth is equal to the radius, though the diagram shows it not quite full.

Correct answer by Adrian Howard on June 14, 2021

R.W. Bird · Answer

If the pressure was lower at other points along the bottom, water wold flow horizontally until it was equal. (You do have to consider the vertical component of the reaction force from upper sections of the container.)

Answered by R.W. Bird on June 14, 2021

Why is pressure $rho g R$ at all points on the base of this upside-down container

2 Answers

Add your own answers!

Ask a Question