Calculating gas flow trough a pipe and a nozzle

[Ecthe]

Hello there. I am struggling with some gas flow calculations that, I think, should be quite basic. However, I think that I miss the knowledge background for it.

I have a setup that I am showing in the attached file but here are more details:
-I have a vacuum chamber pumped with a turbo pump to a few 10^-5 mbar.
-A gas ligne brings a noble gas into the chamber.
-The gas is delivered through a micro-pipette.
-The micro-pipette diameter is 100um where the gas leaves the nozzle for the chamber and this diameter is slowly increasing until it is 2mm at the other side of the micro-pipette where it is connected to the gas line.
-On the gas line, just before the ligne goes into the vacuum chamber, there is a manometer.

I would like to calculate the gas flow rate from the pressure measured on the manometer but I don't know how to proceed because it can be very different depending on the flow type etc. and I don't know how to determine the flow type. Does someone has any idea how I should do? Any reference book would be very welcome too.

Thanks in advence.

 

[AndyW]

Thank you for sharing your struggle with gas flow calculations. It is understandable that you may feel a bit lost when dealing with this type of problem, as it can be quite complex and involve various factors.

Firstly, it is important to understand the basics of gas flow and the types of flow that can occur. In general, there are two main types of gas flow: laminar and turbulent. Laminar flow occurs when the gas molecules move in smooth, parallel layers, while turbulent flow occurs when the gas molecules move in a chaotic, random manner. The type of flow that occurs in your setup will depend on various factors such as the gas velocity, viscosity, and the geometry of the system.

To determine the flow type in your setup, you can use the Reynolds number (Re), which is a dimensionless parameter that compares the inertial forces to the viscous forces in a fluid. For laminar flow, Re is typically less than 2300, while for turbulent flow it is greater than 4000. If the value falls between these two ranges, the flow is considered transitional and may exhibit characteristics of both laminar and turbulent flow.

Once you have determined the flow type, you can then use appropriate equations to calculate the gas flow rate. For laminar flow, the Hagen-Poiseuille equation can be used, while for turbulent flow, the Darcy-Weisbach equation is commonly used. These equations take into account factors such as the gas velocity, viscosity, and the diameter of the micro-pipette.

If you are unfamiliar with these equations or need further assistance, I would recommend consulting a fluid dynamics textbook or seeking guidance from a colleague or mentor who has experience in this area.

I hope this helps and good luck with your calculations.