Pressure needed inside an Air Mattress to deflate in given time

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To determine the pressure needed to deflate an air mattress with a small hole in 2 seconds while applying an external pressure of 28,000 Pa, the discussion highlights the challenge of finding the right equations, as traditional fluid dynamics equations like Bernoulli's may not apply directly to gases in this context. The volume of the mattress is clarified to be 4.4 m³, which significantly impacts the calculations. Participants emphasize the need to consider the flow rate through the orifice created by the hole, as well as the pressure drop across it. The conversation reveals a misunderstanding of the volume initially stated, which could lead to unrealistic expectations regarding air flow rates. Accurate calculations will require a suitable approach to estimate the pressure drop and flow dynamics.
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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!
 
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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...
 
Woops! You're right, I messed up, I meant to type 4.4 meters cubed, not 44. Thanks for the reply!
 
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