Compressible vs. Incompressible Flow Equations

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In fluid dynamics, the distinction between compressible and incompressible flow becomes crucial at Mach numbers around 0.3. For compressed air systems operating at pressures up to 7 bar, the applicability of incompressible flow equations depends on the air's velocity and pressure range. Flow choking can occur at these pressures, indicating that Mach 1 might be reached in certain areas, which complicates the use of standard incompressible equations. Without detailed information about the system's flow characteristics, it's challenging to determine if incompressible equations are adequate. Therefore, careful consideration of flow conditions is essential for accurate calculations in compressed air systems.
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As a private study I'm trying to figure out fluid dynamics applied to compressed air systems. Most of the material I am studying considers only incompressible fluid flow. From what I understand about the differences between compressible and incompressible flow in terms of the equations it only becomes significant when the mach number reaches about 0.3

In my systems I'm dealing with working pressures of no greater than 7 bar. Can apply standard equations to my calculations without having to compensate for changing densities due to pressure?
 
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That depends entirely on how fast the air may move in your system and the range of pressures you plan to operate in. You haven't really described anything in enough detail to know that.
 
At pressures of up to 7 bar, you could very easily have flow choking in places (in other words, locations in the flow where M = 1), so with the information provided, it's impossible to say whether incompressible equations will suffice or not for your purposes.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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