Liquid in a Rotating Cylinder - Pressure

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Discussion Overview

The discussion revolves around calculating the pressure exerted by a fluid inside a rotating cylinder. Participants explore the effects of rotation on fluid dynamics, specifically focusing on the pressure distribution and the forces acting on the fluid in a cylinder with a specific geometry and fluid mixture.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Kim asks how to calculate the pressure exerted by a fluid in a rotating cylinder.
  • CS provides a formula for pressure that includes variables such as the specific weight of the fluid, rotational speed, and height above the origin.
  • Kim expresses confusion about the units of omega squared and seeks clarification on this point.
  • Kim later adds details about the cylinder's dimensions and the fluid mixture, indicating a need to determine the force at a specific area where a pin acts like a piston.
  • A participant questions what specific calculation Kim is trying to perform, indicating a need for further clarification.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and remains unresolved, particularly regarding the calculations needed for the specific scenario presented by Kim.

Contextual Notes

Participants have not reached consensus on the calculations required for the specific geometry and fluid conditions described. There are also unresolved questions about unit consistency in the provided formula.

Who May Find This Useful

This discussion may be useful for individuals interested in fluid dynamics, particularly in applications involving rotating systems and pressure calculations in engineering contexts.

kimkat
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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
 
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kimkat said:
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:

[tex]p = p_0 + \omega^2 \frac{\gamma r^2}{2g} - \gamma y[/tex]

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
 
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!
 
Welcome to PF!

Hi Kim! Welcome to PF! :smile:
kimkat said:
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 :wink:)

ω, the rotational speed (or angular velocity), is in radians per second. :smile:
 
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!
 
How can you calculate what?
 

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