Compressed air in a big tank flows from a little hole. How to judge the choking? If I only know the pressure of the air in the tank and out of the tank?

Many thanks.

Dear Erick,

It is not a very tough job. The pressure in the compressed tan is time-dependent and hence the stagnation/tank pressure is a function of time. Now choking occurs when the pressure outside the tank is nearly half the tank pressure(Of course with 1-d isentropic approximations assumed implicitly). The rate of change of mass within the tank is equal to the mass flow rate through the hole, whicch gives a ODE in time. Making use of isentropic relations and suitable initial conditions, this can be onverted to time-dependent ODE for pressure in the tank. The solution, which may be little complicated will tell you the time histroy of the tank pressure and subsequently when the choking will occur. Note that beyond choking case the ODE is not valid in strict sense, since then the mass flow rate is constant.

Hope this helps

Regards,

Ganesh

Dear Mr. Ganesh, Thank you for giving the solution to my question in details.

(1) From p*/p0=0.528, I may judge the choking state.

But it didn't consider diameter of the little hole.

If the hole is small I can image the choking, but if the

hole turns "big", how to consider this question.

In my case,

in tank: 0.50445 MPa(absolute) , 280.5 K

air : 0.10445 MPa , 289.8 K

diameter of the hole: 0.7 mm Maybe there is a choking in my case?

(2)By the way, I use flow meter to measure the flowrate, when I can the air pressure in tank from 0.20445 MPa to 0.50445 MPa with an interval 0.1 Mpa, the flow rate changes from 2.6 to 4.0 m^3/h.

Best Regards Erick

Dear Erick,

The diameter of the hole defintiely comes into play in predicting the choking. The diameter determines the are and hence the mass flow rate. In your case, rough calculations show that the choking will occur when tank pressure is nearly 0.2 Mpa, but the time instant this happens will be determined by the mass flow rate and hence the hole. Please note that choking is not associated with a "small area", as you would recall for a nozzle, it essentially is a phenomenon that results in constancy of mass flow rate. The "bigness" of the hole is not an issue, though there will be a difficulty to imagine.

I am not an experimentalist, so I am not sure about your second comment, but definitely I would suggest that the interval be reduced, so that you can see to some extent the constancy of mass flow rate after tank pressure drops to 0.2 Mpa

Remember that these are 1-D isentopic calculations and the actual solution could deviate depending on the extent the assumptions are invalid, but a rough picture should emerge.

Hope this helps

Regards,

Ganesh