Liquid in a Rotating Cylinder - Pressure

[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

 

[stewartcs]

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

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
r is the radius
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

 

[kimkat]

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

 

[tiny-tim]

Welcome to PF!

Hi Kim! Welcome to PF!

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

(have an omega: ω )

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

 

[kimkat]

OK, I've been considering this problem so more and I have some more information to add.

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?

Please help!

 

[Dr.D]

How can you calculate what?