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# Air volume passing through a hole

## Air volume passing through a hole

(OP)
What is the maximum volume of air that can pass through a 1 mm hole.  The material through which the air is passing is stainless steel with a .25" wall thickness. I don't believe it is relevant but the air is being sucked through rather than pushed through the hole.

Can you point me to an online calculator for similar queries.

THX.

Dale

### RE: Air volume passing through a hole

dale,

the "maximum" volume of air (or anything for that matter) that can pass through a hole (any size) is infinite.

however, in your case it is finite 'cause it's driven by the pressure differential.  if you're after volume/second then you need the area (of the hole) and the speed of the air (A*V = m^3/sec).

speed depends on the pressure differential, delta P = 1/2*rho*V^2, where rho is the density of air, something like 1.2 kg/m^3 (make sure you have mass density).

the tricky part is the "coefficient of discharge" of the hole.  google this, the engineer's toolbox link gives a table that may help. or the mcnallyinstitute link for "flow through an orifice" ... but be careful with the equations that are posted about, most of them deal with flow out of a bucket (flow is driven by the pressure head).

the ease of finding these links makes me wonder what googling you did on your own ??

### RE: Air volume passing through a hole

However at sufficiently high pressure ratios the hole will choke due to the formation of shock waves, effectively limiting the maximum flow rate (or probably, more accurately, the  flow rate/increase in pressure curve will approach some assymptotic value). Big problem in engine design.

Cheers

Greg Locock

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### RE: Air volume passing through a hole

Hi

The maximum flow of air through a hole will be fixed when it chokes. If I remember correctly the max pressure ratio is 1.8 for air. You can check this is any compressible flow text book.

The previous reply of p = 1/2 rho v^2 is strictly speaking for incompressible flow and is only really valid when mach no (M) < 0.3. Choking occurs when M = 1.

Hope this helps.

allan

### RE: Air volume passing through a hole

mmm, be careful about the definition of choking. Its true definition is when no downstream pressure reduction further increases the mass flow through the 'nozzle'. increases in the upstream pressure, although not increasing the velocity at the throat (M=1 and assuming constant temp) fixes U but rather upping the supply pressure ups the density, and hence your mass flow can increase.

If we could treat it as a simple nozzle then:
work out your pressure ratio, if its greater than 1.895, (simple ratio of gamma) then its choked. then;
Calc , static temp at the throat (M=1), do a search for isentropic flow equations , nasa site should pop up.
M =1 at the throat, and static temp gives you your velocity. (M= U/a , a = root , (gamma* R* Ts)
Calc static density at throat as well.
m dot  = density* area * U

### RE: Air volume passing through a hole

I've finally got round to writing a program that will solve this problem, check out caided.co.uk , and you can download it. I've used VB for it and it needs MS office.
The calculation is the wrong way around for this particular problem, i.e. you give it a mass flow and it calculates the area but you should be able to work backwards. Next upgrade is to enable the user to switch this.

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