# Calculating gas flow trough a pipe and a nozzle

• I
• Ecthe
In summary: Your name]In summary, the forum user is seeking help with gas flow calculations for a setup involving a vacuum chamber and a gas line. They are looking for guidance on how to determine the flow type and calculate the gas flow rate. The suggestion is to use the Reynolds number to determine the flow type and then use appropriate equations such as the Hagen-Poiseuille or Darcy-Weisbach equations to calculate the gas flow rate. Further assistance can be found in fluid dynamics textbooks or through consulting with someone experienced in this area.

#### 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.

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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.

## 1. How is gas flow rate through a pipe and nozzle calculated?

The gas flow rate through a pipe and nozzle can be calculated using the Bernoulli's principle, which states that the total energy of a fluid remains constant along a streamline. This principle is applied to the conservation of mass and energy equations to determine the gas flow rate.

## 2. What are the factors that affect gas flow rate through a pipe and nozzle?

The factors that affect gas flow rate through a pipe and nozzle include the diameter of the pipe or nozzle, the pressure difference between the ends of the pipe or nozzle, the viscosity of the gas, and the length of the pipe or nozzle. Other factors may also include the temperature and density of the gas.

## 3. Can the gas flow rate through a pipe and nozzle be changed?

Yes, the gas flow rate through a pipe and nozzle can be changed by adjusting the pressure difference or by changing the diameter of the pipe or nozzle. The gas flow rate can also be affected by altering the length or viscosity of the gas.

## 4. What is the difference between laminar and turbulent flow in gas flow through a pipe and nozzle?

In laminar flow, the gas particles move in a smooth and orderly manner, while in turbulent flow, the gas particles move in an irregular and chaotic manner. The flow type can affect the gas flow rate and can be determined by the Reynolds number, which is calculated using the gas properties and the dimensions of the pipe or nozzle.

## 5. How can the gas flow rate through a pipe and nozzle be optimized?

The gas flow rate through a pipe and nozzle can be optimized by selecting the appropriate diameter and length of the pipe or nozzle, as well as by maintaining a consistent pressure difference. It is also important to consider the properties of the gas and the potential for turbulence in order to achieve an efficient gas flow rate.