Compressible Fluids: Getting Desired Volume/Mass Flow Rate

In summary: It would also be helpful to consult with someone experienced in compressible fluid systems for further guidance. In summary, the conversation discusses a design for a system that will feed helium through tubing at a desired flow rate and hit Mach 1 at the outlet. The speaker has used Fanno Flow equations to calculate an inlet pressure of 1.9 psig, and is seeking confirmation on whether this is a reasonable pressure to achieve the desired flow rate. They are also open to any additional advice or expertise on the topic.
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I'm having trouble calculating the required pressure to get the desired volume flow rate (at outlet conditions). I'm no expert at compressible fluid systems, but I ended up being the one to design it...

The system must feed helium vertically through 3/8" ID, 112 ft long tubing (ID can vary, I just chose 3/8" for the availability of very lightweight tubing). The desired flow rate is 100 ft3/min or greater (Outlet Pressure = 0.1083 psig). It would be nice to maximize this and hit flow speeds of Mach 1 at the outlet.

So far, I have used Fanno Flow equations and found an inlet pressure of about 1.9 psig. The flow rate here came out to about 100 ft3/min. Does this pressure make sense? It seems a bit low to me... especially to hit Mach 1.

Am I headed in the right direction at least? If anyone has experience with this, any help would be appreciated, Thanks.
 
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  • #2
It is possible to achieve Mach 1 at the outlet with an inlet pressure of 1.9 psig, depending on the exact length of the tube and the exact internal diameter of the tubing. However, it is likely that the actual flow rate achieved at that pressure would be lower than 100 ft3/min due to frictional losses, so you may need to increase the inlet pressure slightly to achieve the desired flow rate. You could use a combination of the Fanno Flow equation and the isentropic flow equation to calculate the required pressure.
 

1. What is a compressible fluid?

A compressible fluid is a type of fluid that can change its volume when subjected to pressure or temperature changes. Examples of compressible fluids include gases, such as air, and some liquids, such as carbon dioxide.

2. How do you determine the desired volume flow rate of a compressible fluid?

The desired volume flow rate of a compressible fluid can be determined by using the ideal gas law, which states that the volume of a gas is directly proportional to its temperature and inversely proportional to its pressure. By manipulating this equation, the desired volume flow rate can be calculated.

3. What is the mass flow rate of a compressible fluid?

The mass flow rate of a compressible fluid is the amount of mass that passes through a given area per unit of time. It is determined by multiplying the density of the fluid by the velocity and the cross-sectional area of the flow.

4. How can the desired mass flow rate of a compressible fluid be achieved?

The desired mass flow rate of a compressible fluid can be achieved by adjusting the pressure or temperature of the fluid. This can be done by using devices such as compressors, pumps, or heaters to increase the pressure or temperature of the fluid, which will result in a higher mass flow rate.

5. What factors can affect the volume or mass flow rate of a compressible fluid?

The volume and mass flow rate of a compressible fluid can be affected by several factors, including temperature, pressure, density, and velocity. Changes in any of these variables can impact the flow rate of the fluid. Additionally, the physical properties of the fluid, such as viscosity and compressibility, can also play a role in determining the flow rate.

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