Pressure in a rotating cylinder

In summary, the conversation discusses a space station consisting of a spinning cylinder filled with air, and the ratio of air pressure at the center to the rim is being questioned. The ideal gas law and a suggested online resource are mentioned as potential starting points for solving the problem.
  • #1
SonOfOle
42
0

Homework Statement


A space station consists of a large cylinder of radius [itex]R_0[/itex] filled with air. The cylinder spins about its symmetry axis at an angular velocity of [itex]\Omega[/itex] providing a centripetal acceleration of [itex]g[/itex] at the rim of the cylinder (at [itex]R_0[/itex]).

If the temperature is constant inside the station, what is the ratio of the air pressure [itex]P_c[/itex] at the center of the cylinder to the air pressure at the rim [itex]P_r[/itex]? (Treat the air as an ideal gas with each gas particle having a mass of [itex]m[/itex].


Homework Equations


PV=NRT...


The Attempt at a Solution


This is beyond where I know what to start with. Could someone point me in a good direction? (or know of a place online or in textbooks that I could look up how to approach problems like this?)

Thanks,
 
Physics news on Phys.org
  • #2
Take a look at question one in this page. There's a solution in PDF and PS formats (Czech language).

http://fykos.troja.mff.cuni.cz/index.php?id=2&serie=5&volume=21&lang=en&" [Broken]
 
Last edited by a moderator:

1. What effect does rotation have on pressure in a cylinder?

Rotation in a cylinder can cause pressure to increase at the outer walls and decrease at the inner walls. This is known as the centrifugal effect, where the faster moving particles on the outer edge of the cylinder experience a greater force and thus have a higher pressure.

2. How does the shape of the cylinder affect pressure?

The shape of the cylinder can impact pressure distribution. A longer, thinner cylinder will have a larger centrifugal effect, leading to a greater pressure difference between the outer and inner walls. A shorter, wider cylinder will have a smaller effect and a more even pressure distribution.

3. How does fluid viscosity affect pressure in a rotating cylinder?

Fluid viscosity refers to the thickness or resistance of a fluid to flow. Higher viscosity fluids have a greater resistance to the centrifugal effect, resulting in a more even pressure distribution throughout the cylinder. Lower viscosity fluids will experience a larger pressure difference between the outer and inner walls.

4. Can the speed of rotation affect pressure in a cylinder?

Yes, the speed of rotation can have a significant impact on pressure distribution in a cylinder. Higher rotational speeds will result in a stronger centrifugal effect and a greater pressure difference between the outer and inner walls. Lower speeds will have a smaller effect and a more even pressure distribution.

5. How is pressure in a rotating cylinder related to the Coriolis effect?

The Coriolis effect is a result of the rotation of the Earth and its impact on moving objects. In a rotating cylinder, the Coriolis effect can cause a shift in pressure gradients, resulting in uneven pressure distribution. This effect is more pronounced in larger cylinders with faster rotation speeds.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
1K
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
633
Replies
7
Views
481
Replies
1
Views
504
  • Mechanical Engineering
Replies
2
Views
2K
  • Introductory Physics Homework Help
4
Replies
116
Views
3K
  • Mechanical Engineering
Replies
3
Views
877
  • Mechanical Engineering
Replies
8
Views
1K
Replies
5
Views
501
Back
Top