Pressure needed inside an Air Mattress to deflate in given time

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SUMMARY

The discussion focuses on calculating the necessary internal pressure of an air mattress to achieve deflation within 2 seconds while a weight applies an external pressure of 28,000 Pa. The air mattress has a volume of 4.4 m³ and a hole with a diameter of 2 cm for air escape. Participants highlighted the need for equations related to pressure drop across an orifice and flow rate estimation, suggesting that Bernoulli's equation may not be applicable for compressible fluids like gases. The importance of accurately determining the volume and flow dynamics was emphasized to avoid unrealistic scenarios.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically orifice flow.
  • Familiarity with the ideal gas law and its limitations.
  • Knowledge of Bernoulli's equation and its application to incompressible versus compressible fluids.
  • Basic concepts of pressure measurement and flow rate calculations.
NEXT STEPS
  • Research orifice flow equations to calculate pressure drop and flow rate.
  • Study the application of the ideal gas law in dynamic scenarios.
  • Explore compressible fluid dynamics and relevant equations for gases.
  • Investigate the effects of external pressure on gas flow through small openings.
USEFUL FOR

Students in physics or engineering, particularly those studying fluid dynamics, as well as hobbyists working with inflatable structures and anyone interested in practical applications of gas laws and pressure 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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