Conservation of Mass Question

[Red_CCF]

Hi

Just a quick question about Conservation of Mass that I somehow managed to confuse myself:

If I have a vent of constant cross section at steady state, given that conservation of mass means that inlet and exit mass flow rate must be the same, does this mean that, taking the compressibility of gas into account (for this example I'm assuming Ma > 0.3 although unrealistic in real life), this means that the exit velocity must be greater than the inlet velocity (temperature and pressure are the same in inlet and exit)?

Basically my question is (and I know this sounds stupid), conservation of mass holds always even if the gas is compressible?

Thanks

 

[olivermsun]

Conservation of mass always holds.

In your example, "steady state" would usually mean that mass (and hence gas pressure) aren't building up between the inlet and the exit.

 

[Bob S]

Use grams per second as flow rate.

 

[Red_CCF]

Conservation of mass always holds.

In your example, "steady state" would usually mean that mass (and hence gas pressure) aren't building up between the inlet and the exit.

Hi

So at steady and the gas is flowing very fast such that it becomes compressed by the time it gets to the outlet (so its density is higher at the outlet than inlet). Keeping P and T known and constant and area as constant, then the gas velocity at the outlet and inlet are related by the inlet density/exit density = exit velocity/inlet velocity? And the ideal gas law can be used to relate the densities (assuming the P and T conditions are ideal enough)?

Thanks

 

[alphy]

Hello,

Thank you for your question. Conservation of mass is a fundamental principle in physics that states that mass cannot be created or destroyed, only transformed into different forms. This applies to both compressible and incompressible fluids, including gases. Therefore, in your example of a vent with constant cross section, the mass flow rate must be the same at both the inlet and exit, regardless of the gas's compressibility. This means that if the inlet and exit have the same temperature and pressure, the exit velocity must be greater than the inlet velocity in order to maintain a constant mass flow rate. This is due to the fact that the density of a compressible gas decreases as its velocity increases, so a higher velocity is needed to maintain the same mass flow rate. I hope this clarifies your confusion. Please let me know if you have any further questions.