# Pressure at the bottom of a container

Before I ask my question, I would like to clarify that this is NOT a homework question. Rather I would like to clear up an issue with my intuition about fluid statics using this problem. Firstly, I feel like there can't be any pressure on the bottom of container C as if the container is a perfect triangle with sharp edges, there wouldn't be any perpendicular surface to have pressure, so how would I go about finding the pressure at the bottom of container C?

Secondly, I am unsure why and how changing the volume of the container would change the pressure at the bottom. I feel like these problems are arising due to my misunderstanding on how pressure works, hence I would like to clarify these gaps in my intuition. Thanks!

Note that the answer to part (a) is all 3 containers have the same pressure at the bottom (which I don't see why). The answer to part (b) is $$A (which I don't see why either).

• Is this an AP Physics 2 released test question? Commented Jul 5, 2020 at 15:48
• @DavidWhite I am not sure, my proffessor just gave us this question in a test. Commented Jul 5, 2020 at 16:11
• OK. Hopefully, my answer enlightened you regarding the correct answers to this problem. Commented Jul 5, 2020 at 16:13
• I definitely see my misconception with the help of all the answers, pressure is a function of only height, density and gravitational acceleration, I see why I shouldn't need to worry about the surface properties or orientation : ) Thanks all Commented Jul 5, 2020 at 16:18

The hydrostatic pressure under a water column is ONLY dependent on the height of water above that point, and is independent of the shape of the container holding that water, per the equation $$P=\rho g h$$. That pressure is always exerted perpendicular to whatever surface the liquid encounters, so the surfaces of object "C" do indeed experience a pressure, but the force from that pressure is NOT directed sideways or downward because the sides of object "C" are nor vertical or horizontal.

Regarding the answer for item "ii", the objects are filled to a volume of V/2. In looking at the objects, it is apparent that when this is done, water will rise to a low height in object "A" because most of the volume exists in the base of this object, water will rise to half the height of object "B" because this object has vertical sides, and water will rise to a height that is greater than half of the object's height for "C", because most of the volume of this object is contained in the top of the object. Because the height of the water in the objects will be in the order of A<B<C, the hydrostatic pressure at the bottom of each object will also be in this order, per the equation $$P=\rho g h$$.

Your confusion is understandable! In Wikipedia, for example, pressure is defined as "Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed."; and it is entirely natural to think that there is an intimate and necessary connection between "pressure" and a "surface".

However, that definition of pressure is inadequate. Pressure exists whether or not there is a surface to experience the forces of pressure. It is an aspect of the condition of the fluid at any and every point in the fluid; and it exists throughout the fluid.

The reason definitions of pressure mention surfaces is that one way to measure pressure is to introduce, for example, a piston whose front face (a surface) is exposed to the fluid pressure, and whose back face is exposed to vacuum. The force exerted by the fluid against the piston, divided by the area of the piston's face, is equal to the pressure in the fluid.

However, there are other ways to measure pressure that do not involve a surface at all. For example, if the fluid is a gas it is subject to the Ideal Gas Law. From the Ideal Gas Law, the pressure $$P$$ at any point can be determined by measuring the temperature and density of the gas.

Changing the volume of the container in your example does not affect the pressure at the bottom of the container, but any change in shape that changes the height of the fluid will change the pressure at the bottom because the pressure is proportional to the height of fluid above the bottom (if the fluid is incompressible like water).