Calculate flow rate of air through a pressurized hole I was wondering about this: If there is a

Brooklynn Hubbard 2022-05-18 Answered
Calculate flow rate of air through a pressurized hole
I was wondering about this:
If there is a pressurized container, like a tank of compressed air at some pressure that is greater than the ambient air pressure, and this tank of air has a hole in it, what is the velocity of the escaping air through the hole? Is there a formula for this?
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Answers (1)

Superina0xb4i
Answered 2022-05-19 Author has 17 answers
If you neglect viscosity, Bernoulli's equation (just Navier-Stokes without frictional or stress terms) will get you into the ballpark:
P g + 1 2 ρ g v g 2 = P a
Where the g subscripts pertain to the gas and the a subscript to the ambient. The gas density ρ g M / V is the ratio of the mass of gas (M) in the tank to the volume of the tank. If the tank is a rigid container (like a propane tank) then the volume of the gas is constant and the pressure will vary with the mass flow and the temperature. If you assume the tank remains at a constant ambient temperature, the pressure will only vary with the mass flow rate (isothermal expansion) and you can obtain that from the ideal gas law:
P g = m M R T
where m is the molecular mass of the gas in question, T the temperature, R the gas constant, and M the total mass of the gas remaining in the tank. This is a function of time because mass is leaving the tank. The rate at which mass leaves is a function of the exit velocity (it depends on the volumetric flow rate, which is a product of the exit orifice size and the exit velocity). So you can solve for M ( v g ) and substitute in the above equations and solve for v g self-consistently. Note this approach also ignores any pipes that might be attached to the orifice. For that, you'd need to calculate the volumetric flow rate using Poiseuille's equation.
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