Dynamics of pumping fluid into a cylinder with an air hole?

[Hepth]

I should be able to do this, but its been a while and maybe I'm making this more difficult that it should be.

Assume you have a cylinder nearly sealed but with an outlet hole at the top. I want to pump a fluid into the canister, pushing the air out of the hole, and time how long it takes. The ultimate goal is to try and see what size the hole is, or even what its flow coefficient (if flow rate Q = Area*velocity*K)

What is the simplest way to go about this calculation? I have attached an image, the outlet hole can go anywhere. Let's say that I can control the pump's flow rate or pressure, and the air starts at 1atm both inside and outside.

What is the best approach? By work done? By number of air molecules escaping? By force balancing?

Thanks!

Any ideas?

 

[Nidum]

If you can control the pump flow rate then this is a non problem ?

 

[Hepth]

Sorry, let's say that I can command a pressure only rather than flow rate.

 

[Nidum]

In that case the fluid is only acting as a liquid piston . Pressure in the air space is same as in fluid . Air flow from hole is given simplistically by Bernoulli equation though much more accurate calculations are possible for specific conditions of flow .

 

[Svein]

I used something similar 40 years ago. The "air hole" was a small valve. The object was to fill a "tank" with water using a centrifugal pump (large capacity, but could only create about 2 atms of pressure) and then change over to a piston pump (low capacity, but high pressure). Looking up basic physics, I used a pressure sensor mounted right inside the "hole" and waited for the pressure to rise rapidly (at that moment there was no air left inside).