# Homework Help: Centrifugal force in high pressure vessel

1. Oct 19, 2004

### drewman13

An enclosed cylindrical* (disc) vessel one inch thick and five inches in radius holding two pounds of fluid at ambient atmospheric pressure (14psi?)and being spun at 30,000 rpm's. Assume the centrifugal force acting on the fluid creates a pressure of 1,000 psi. The question is ....

"If the vessel is pre-pressurized, to say 3,000 psi, before it is spun up to 30,000 rpm's, will the centrifugal force add pressure to the already pre-pressurized (3,000 psi) vessel?"

Would the resultant force then be 4,000 psi? If not, what would the total psi be and why?

2. Oct 20, 2004

### aekanshchumber

Use Dalton's partial pressure law.

3. Oct 20, 2004

### Tide

He didn't say the vessel was pressurized with gas.

4. Oct 20, 2004

### aekanshchumber

If it is so, then the pressure of the gas will depend on the position from where it is being measured.
Due to rotations, the gas will be displaced toward the outer side. And the pressure of the gass will gradually increase when we move from ceter of rotation to the extreme of the daimeter.

5. Oct 20, 2004

### Clausius2

Yes, I'm with aekanshchumber, and I'll give him an additional support for his opinion writing a few equations:

Inside the vessel, and choosing a reference frame spinning with it, the Navier-Stokes equations yield:

$$\frac{\partial P}{\partial r}=\rho\omega^2 r$$ in Hydrostatic form.

Solving for P(r) you will obtain the pressure distribution. The constant resulting of the last equation has to depend on the initial value in the case of a closed vessel, where no boundary constraint is possible to satisfy.

Maybe, the unsteady process is harder [\B] of analyzing due to a progressive acceleration of the fluid is necessary. The kinematic field has to be solved firstly before doing any comment about the pressure at the very first instants. I don't think such a simple rule as drewman13 has stated would be correct for figuring the total pressure out.

6. Oct 20, 2004

### snbose

The pressure will surely increase, but it will not be 4000psi.

Remember that the pressure is proportional on the no of molecules. So for a fixed volume (of the cylinder, V) at 1.4psi if the Number of moecules be N, then at 3000 psi it will be around 2000N.

Now if N molecules generated a 1000psi pressure when gyroscoped @ 30000rpm, then 2000N molecules will generate 2000 x 1000psi at same rpm. I imagine they are proportional however they may not be directly proportional. But logically and from Classical kinetic theory they are likely to be directly proportional.

So you can imagine the net pressure to be humongous 2,000,000 psi.

7. Oct 20, 2004

### sal

The logic sounds good but the starting pressure was 14 psi, not 1.4 psi.

So, 3000 psi ---> 200N, not 2000N, and the final pressure will be 200,000 psi.

8. Oct 20, 2004

### snbose

OPPS..thanks for correcting me.