Flow through an orfice, calculations?

Style

Hi!
Any one have any formulas for calculating what size I should have on an orfice if I want for example a flow of 0.5 liter O2 per minut? I know I will have to have an un-deep compensationg regulator if I want a constant flow so what I'm after is just the formulas.

/Edvin

brinoz

You can use this simulator

Free Flow and Orifice Calculations by LENOX LASER - Online Orifice Sizing Calculator

Regards
Bruno

Style

Thanks alot for that link, really use full. But still it would be fun to see the calculations behind it.

gibbogeo

Maybe this helps:

Flow Control Mathematics by LENOX LASER - Laser drilling, aperture, orifice and microhole leader

oxyhacker

There's a formula on our website, see:

http://airspeedpress.com/gallery.html

at the bottom of the page

deanc

The calculation goes :-
mass flow (kg/s) = area (m2) x density (kg/m3) x velocity (m/s)

Since it will be choked flow, we would need to calculate :-

1. Temperature
2. Pressure
3. Density
4. Mach number in the orifice (Ma=V/c) actual velocity divide speed of sound

Then simply convert the mach number to an actual velocity and multiply out for the the mass flow rate.

I scanned one short example, with two cases :-
a) non-choked flow (where downstream pressure WILL affect the mass flow rate)
b) choked flow (where downstream pressure WILL NOT significantly affect the mass flow rate)

For the breather the calculation is very similar.

Molecular weight (hence mass flow via density), and specific heat ratio (k=cp/cv) would be the drivers for different mixes.

Regulator pressure and ambient depth pressure would be the drivers for pressure relations.

Look for any fluid dynamics textbook with incompressible flow, there is plenty of description in the text and derived equations with explanation before you get to the examples...

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jradomski

Don;t forget you have to take into account what gas the flow meter was designed to read.. If themeter was calibrated for aie it will have an error in it when measuring Oxygen and vice versa.. You will need to make corrections based on the specific gravity of the gas..

__________________
Joe Radomski
CCR Trimix Instructor Trainer
ANDI Instructor Trainer Director #10

All posts are personal opinions and DO NOT reflect any affiliated agency unless specifically stated.

deanc

That looks horrible.

upstream 101 kPa, standard temperature 25 C
Diameter 11.3 mm

a) downstream 80 kPa
Mach number = 0.587
Density = 1.04 kg/m3
Temperature = 269 K (-4 C)
Velocity = 193 m/s
Mass flow rate = 20.1 grams per second

b) downstream 40 kPa
Mach number = 1
Density = 0.780 kg/m3
Temperature = 240 K (-33 C)
Velocity = 310 m/s
Mass flow rate = 24.2 grams per second

Freef

You may also need to work out the critical ratio for the pressures involved so that you maintain a sonic flow through the jet. If you use a depth compensatig first stage you will keep the flow for longer.

http://www.rebreatherworld.com/semi-...tml#post114933

touches on the subject and has a scary formula and some further reading references.

__________________
David.

Diving the mahogany rebreather.

deanc

Yes the critical pressure ratio is worked out in the example. For air at k=1.4 it is 0.528. It is found by substituting Ma = 1, k = 1.4 into the pressure equation. Oxygen at 1 atm and 15 C also has k = 1.40.

Do you have data (an actual table or plot?) on how the interstage pressure varies with depth down to say 150 m? Even for one reg, given different piston areas amongst models etc. With actual data, I can see a simple plot coming along, depth versus IP and downstream pressure -> plot mass flow versus depth, for generic orifice sizes. Detailed calculation.

Hence I could plot generic curves for the common orifice sizes. What are common orifice sizes off the shelf for somehting like the KISS?

All flow will be compressible (changes in density > 10% from inlet to outlet), not necessary to be choked (your term sonic). Pressure drop ratio of less than 0.528 will be compressible but sub-sonic flow. This would occur at depth, where the downstream pressure is more than 0.528 times the IP pressure. 11 ata inlet, 7 ata outlet (60 m) would not be choked, so example (a) would apply. 11 ata inlet, 4 ata outlet (30 m) would be choked, so example (b) would apply.