Pressure needed inside an Air Mattress to deflate in given time

[hunnedlicks]

Homework Statement

I am trying to figure out what pressure I need inside an air mattress if I want it to deflate in a given time and given also that I'm applying pressure on it. Basically, I have an air mattress with a small hole in it for air to come out of, and I need to figure out how much pressure I need inside of it if I want to completely deflate it in, let's say, 2 seconds by dropping a weight on it (which will apply some pressure on the mattress). The mattress doesn't not stretch (is not elastic); it's volume is 4.4 m^3. The time I want the mattress to deflate in is about 2 seconds. The Pressure I will be applying on the mattress over those two seconds is about 28000 Pa. I will be filling the mattress with air. The hole has a diameter of 2cm.

Homework Equations

ideal gas law? bernoulli's equation? poiseulle's equation?

The Attempt at a Solution

I tried looking at a version of bernoulli's equation that is supposed to work for compressible fluids, (and therefore gases?), but I don't think it will apply. The ideal gas law doesn't seem to take time into account, so I don't think it will work, at least not by itself. I was hoping there would be an equation like bernoulli's equation or similar fluid dynamic equations but for gases.
I can't seem to find an equation that might be useful, so I don't even know where to start.

Thanks in advance!

 

[cyrustabery]

I can't imagine what you describe is possible. Also i think you may have the volume of your air mattress a bit off. 44 cubic meters is HUGE! If you wanted all that air through a 2cm hole in 2 seconds then it would have to go super sonic!

You are looking for a pressure drop across an orifice and then estimating a flow rate...

 

[hunnedlicks]

Woops! You're right, I messed up, I meant to type 4.4 meters cubed, not 44. Thanks for the reply!