# Liquid in a Rotating Cylinder - Pressure

1. Jan 5, 2009

### kimkat

Hello,

I need some help. I have a fluid inside a rotating cylinder being flung out towards the walls and exerting a pressure upwards. How would I calculate this pressure?

Thank you,

Kim

2. Jan 5, 2009

### stewartcs

Hi Kim,

The pressure at any point is:

$$p = p_0 + \omega^2 \frac{\gamma r^2}{2g} - \gamma y$$

where,

p_0 is the pressure at the origin
gamma is the specific weight of the fluid
omega is the rotational speed
y is the height above the origin

Note the origin is r = 0, y = 0.

Hope this helps.

CS

3. Jan 6, 2009

### kimkat

that helps alot! I just have one more question, my units aren't working out correctly, what are the units on omega^2? Thank you!

4. Jan 6, 2009

### tiny-tim

Welcome to PF!

Hi Kim! Welcome to PF!
(have an omega: ω )

ω, the rotational speed (or angular velocity), is in radians per second.

5. Jan 6, 2009

### kimkat

The cylinder has a diameter of 123mm and has a 50% air and oil mixture in it. There is a pin at the top acting like a piston. The area at the pin is where i need to determine the force.

the oil is flung towards the outside of the cylinder, so it would be reasonable to assume that there is oil only in half the can (1/4 of the diameter on each side of the can). How would I calculate this?