Liquid in a Rotating Cylinder - Pressure

In summary, Kim asked for help calculating the pressure exerted by a fluid inside a rotating cylinder with a pin at the top acting as a piston. The pressure at any point can be determined by using the formula 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, and y is the height above the origin. Omega, the rotational speed, is in radians per second. Kim later provided additional information about the diameter and composition of the cylinder, and requested help calculating the force at the pin area.
  • #1
kimkat
3
0
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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  • #2
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
 
  • #3
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
Welcome to PF!

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

(have an omega: ω :wink:)

ω, the rotational speed (or angular velocity), is in radians per second. :smile:
 
  • #5
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!
 
  • #6
How can you calculate what?
 

1. What is the relationship between pressure and velocity in a rotating cylinder filled with liquid?

The pressure in a rotating cylinder filled with liquid is directly proportional to the velocity of the liquid. This means that as the velocity of the liquid increases, the pressure also increases.

2. How does the shape of the rotating cylinder affect the pressure distribution of the liquid?

The shape of the rotating cylinder affects the pressure distribution of the liquid by creating areas of high and low pressure. The pressure is highest at the center of the cylinder and decreases towards the edges.

3. How does the density of the liquid impact the pressure in a rotating cylinder?

The density of the liquid has a direct impact on the pressure in a rotating cylinder. A higher density liquid will experience greater pressure than a lower density liquid at the same velocity.

4. Does the rate of rotation of the cylinder affect the pressure of the liquid inside?

Yes, the rate of rotation of the cylinder has a direct impact on the pressure of the liquid inside. As the rate of rotation increases, the pressure also increases due to the increase in velocity of the liquid.

5. Can the pressure in a rotating cylinder be controlled?

Yes, the pressure in a rotating cylinder can be controlled by adjusting the rotation rate, density, and shape of the cylinder. The pressure can also be controlled by changing the properties of the liquid, such as viscosity, temperature, and surface tension.

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