Trying to calculate the volume of gas flowing through a nozzle

[bsheikho]

I've gone through many posts but haven't really come across something very clear. And on top of it my knowledge of fluid dynamics only extends to compressible fluids.

I have a Nitrogen Cylinder Tank, with an exit pressure of 214.7 psia which is blocked by a solenoid valve at a location very close to the discharge nozzle (negligible losses through tubing). This gas is discharged into the atmosphere 14.7 psia.

The gas passes through a desiccant air filter which removes majority of humidity in the gas.

The shape of the nozzle is that of a laser cutter: V shaped, with opening at the center, This opening is 1mm in diameter.

Everything is stored at ambient temperatures of 23°C. The temperature of the gas before exiting the nozzle can be assumed to be 23°C since there is a very minimal amount of time for the laser to excite the gas before it exits.

Is there any feasible way to calculate the flow rate of gas exiting the nozzle? The aim is to figure out the volume of gas being consumed over a production time, and eventually the cost of the gas for the production.

Any form of guidance is greatly appreciated.

 

[bsheikho]

Can i assume that the exit speed of the gas will be mach 1: 332m/s. my opening is area of 1mm circle: 7.85 e-7 m2.

Therefore volumetric flow rate Q=VA=(332)(7.85e-7)= 2.61e-4 m3/s= 0.553028 cfm

 

[CKwik240]

Can i assume that the exit speed of the gas will be mach 1: 332m/s. my opening is area of 1mm circle: 7.85 e-7 m2.

Therefore volumetric flow rate Q=VA=(332)(7.85e-7)= 2.61e-4 m3/s= 0.553028 cfm

Why would you assume the gas velocity is mach 1? The velocity is dependent on the flow rate and size of the orifice. And that is dependent on the pressure differential driving the gas through the orifice. You might try calculating this like an orifice plate in a pipe.

 

[bsheikho]

Well, I don't have the flow rate, or the speed. Thats what I'm trying to figure out.

And the assumption was based on some other posts I've read, regarding choked flow.

 

[JBA]

Your assumption is correct because the point of critical (sonic) velocity flow for all gases occurs at all inlet pressures where the out pressure is less than approximately 50% of the inlet pressure. The accurate value varies with the gas composition but for your extreme pressure differential that variance is insignificant.

 

[CKwik240]

That would put us into compressible flow. If the OP only needs the volumetric flow rate at the nozzle (ignoring gas density), the equation should work fine. But if he needs to know how much gas actually passes (scfm or mass flow rate), he needs to consider the density change of the gas, which is still dependent on the pressure differential.

 

[JBA]

Actually, the mass flow is only dependent upon the nozzle inlet pressure for critical flow.

 

[JBA]

I have run your problem through a nozzle flow MSExcel macro program I wrote and used for many years for high pressure relief valve calculations. As you will note the flow volume is in SCFM which is the ACFM x P in (psia) / 14.7 @ 68°F US Standard. See the below screen shot of the calculation. The .975 orifice coefficient is for a well designed flow nozzle so your flow rate could be a lower depending upon the actual coefficient of your nozzle design. For example: If it is a square edged inlet hole then that value could be as low as 0.69 and the results given can be adjusted by multiplying the result by (your coefficient) / .975.

(Note: Ignore the Steam note and subsonic values as they are not relevant to the program's final selected flow condition.)

 

[bsheikho]

Actually, your right, Orifice plate does have a

I have run your problem through a nozzle flow MSExcel macro program I wrote and used for many years for high pressure relief valve calculations. As you will note the flow volume is in SCFM which is the ACFM x P in (psia) / 14.7 @ 68°F US Standard. See the below screen shot of the calculation. The .975 orifice coefficient is for a well designed flow nozzle so your flow rate could be a lower depending upon the actual coefficient of your nozzle design. For example: If it is a square edged inlet hole then that value could be as low as 0.69 and the results given can be adjusted by multiplying the result by (your coefficient) / .975.

(Note: Ignore the Steam note and subsonic values as they are not relevant to the program's final selected flow condition.)

View attachment 105591

WOW! That is wonderful, thank you for taking the time.

When I convert my cfm to scfm, I end up to 4.58 scfm (very close to actual). Just to confirm, the flow orifice coefficient is factored in by dividing scfm by the coefficient?

 

[JBA]

No, the actual flow is: theoretical flow x the orifice coefficient. The coefficient is a correction on the theoretical flow for the fact that no orifice is 100% efficient.

In the above calculation I have applied a .975 factor (which the maximum that ASME allows for flow certified nozzles used in pressure relief valve capacity certification testing) and as a result the theoretical (100% efficiency) flow rate for that case is 4.69 SCFM (my calculated result) divided by .975 = 4.81 SCFM. For any other nozzle coefficient you would multiply 4.81 by that coefficient to get the true projected flow through the nozzle. The equation I gave simply combines those two steps into one calculation. i.e. (4.69 / .975) X (your coef).