# Velocity of pressurized air through a vent?

Suppose I have a tank of air pressurized to, say, 90psi. Now suppose I open a valve on the tank that is 1-inch (0.083 feet) in diameter. How would I calculate the velocity at which air is escaping through that valve? Presumably the velocity would decrease as the loss of air causes a drop in pressure. How would I calculate the velocity for any given momentary pressure? The CFM that would result is unknown, so that cannot be part of the equasion. Thanks.

Update:

With regard to Bomba's answer: Suppose that, for reasons I won't explain, my tank's pressure wil never drop below 60psi. Does your answer mean that I can basically just assume a velocity of 1117ft/sec (sonic velocity) for the duration of the drain from 90psi to 60psi, because the differential will not be reduced sufficiently to require use of the other formula you mentioned?

Update 2:

Paducahbill: Thanks for the answer, but I can't use any measuring instruments. I'm trying to write a computer simulation for something which I do not have first-hand access to. The simulation doesn't have to be perfect, but I do have to rely on known formulas rather than first-hand measurements.

Relevance
• Bomba
Lv 7

EDIT

Yes, it will not diminish below critical for that condition.

And that is as fast as it can go even if the pressure was 1000psig. Sometimes the sonic velocity is called "choking" as well as "critical".

I have supposed that this is a pretty big tank since the valve is 1 inch. If it is a smaller tank, then what I will describe will just happen quicker.

For much of the reduction of this air volume you are going to have critical (or sonic ) velocity. This is a phenomenon of fluid flow which occurs when the pressure difference is over about half of the absolute upstream pressure. In the case of air it is 0.53.

To begin with, your absollute tank pressure will be 105 psia. Half of that is 52psi and the total differential is 75psi. So your velocity will be sonic and will remain sonic until the differential is greatly reduced.

Critical air flow occurs when P2/P1 => 0.53. In this case P2 is always atmospheric 15 psia and P1 will be diminish, even though the critical flow is constant. When P1 = 15 /(0.53) = 28 psia or 13 psig, the velocity and flow will then begin to diminish according to the diminishing pressure differential. This gets a bit complicated.You just do not want to see that equation. ( I just don't want to write it) But by then most of the air is gone anyway. The sonic velocity of standard air is 1117 fps ( Pratt-Whitney)

Note that for air leaking to atmospheric, the velocity will be critical as long as the vessel or pipe pressure is above 13 psig.

Often orifices are placed in critical piping so that if there is a rupture, the leakage will be retarded by the limited velocity through the smaller hole in the orifice plate.

Source(s): Elementary Fluid Mechanics - Vennard, and notes