# Trying to calculate the volume of gas flowing through a nozzle

• bsheikho
In summary, the conversation discusses the calculation of the flow rate of gas exiting a nozzle by taking into account factors such as pressure, temperature, and orifice coefficient. A formula is provided for calculating the volumetric flow rate, and the use of a flow nozzle is suggested for accurate results. The conversation also clarifies the difference between SCFM and ACFM and the importance of considering the efficiency of the orifice in the calculation.
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.

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

bsheikho said:
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.

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.

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.

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.

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

bsheikho
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.)

ERGIN and bsheikho
Actually, your right, Orifice plate does have a
JBA said:
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?

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).

bsheikho

## 1. How do you calculate the volume of gas flowing through a nozzle?

The volume of gas flowing through a nozzle can be calculated by multiplying the cross-sectional area of the nozzle by the velocity of the gas flow. This can be represented by the following formula: V = A x V, where V is the volume, A is the cross-sectional area, and V is the velocity.

## 2. What is the importance of calculating the volume of gas flowing through a nozzle?

Calculating the volume of gas flowing through a nozzle is important for various reasons. It helps in determining the amount of gas that can be processed and transported through a system, which is crucial for industries such as power generation, chemical processing, and oil and gas. It also helps in designing and optimizing the efficiency of nozzles and other related equipment.

## 3. What factors can affect the volume of gas flowing through a nozzle?

Several factors can affect the volume of gas flowing through a nozzle, including the size and shape of the nozzle, the gas properties (such as density and viscosity), the pressure and temperature of the gas, and the presence of any obstructions or restrictions in the flow path.

## 4. How do you account for the compressibility of gas when calculating volume flow rate?

When dealing with compressible gases, the ideal gas law (PV = nRT) can be used to account for changes in volume due to changes in pressure and temperature. Alternatively, more complex equations of state, such as the van der Waals equation, can also be used to account for gas compressibility.

## 5. Can the volume of gas flowing through a nozzle be accurately calculated in real-world applications?

While the volume of gas flowing through a nozzle can be calculated theoretically, in real-world applications, there may be uncertainties and variations due to factors such as turbulence, flow separation, and other external influences. Therefore, it is important to consider these factors and conduct experiments or use empirical data to validate and refine the calculated volume.

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