How do you calculate the pressure of a fluid inside a spinning cylinder?

[mountaintroll]

What I've found online so far just completely boggles my brain right now. I've never been too good with math, but anyway I am trying to learn.

 

[studiot]

Is this homework?

You need to describe it properly and show your working.

If not you still need to describe it properly.

[mountaintroll]

No homework, just me trying to learn things I didn't when I was a kid.

Sorry about that. I'll try this with an example.

If you had a cylinder with an internal radius of lets say 1 foot, and this cylinder is 1 inch wide, and it is rotating at a rate of 1000 rpm while filled with water, how do you figure out how much pressure the water furthest from the center would be under? Hopefully that's clear enough.

[studiot]

OK so a bucket of  incompressible liquid such as water has a free surface (with the air).

The pressure at that free surface is equal to the air pressure there.

Below each point on that free surface the pressure in the column of water has two components, clled the static head and the dynamic head so you need to know which one you are looking for.

This free surface takes on the shape of a parabaloid of revolution if the bucket of water is spun.

The static head is due to the weight of the water above any point in the fluid and varies with depth.

The dynamic head is due to the tangential velocity of the water, which decreases with increasing radius from the centre, but remains constant with depth.