Compressible and Incompressible Flow in Fluid Mechanics

Fluid mechanics is a very important field of engineering. Lots of kinds of engineering systems are designed with the laws of fluid mechanics. In fluid mechanics, the compressible and incompressible flow of fluids is a very important distinction. With this distinction, the laws of fluid mechanics which are applied to solve the fluid problems change. So, it is very important to know the difference between compressible and incompressible types of flow in fluid mechanics. 

In this article, we would like to explain the compressible and incompressible flows in fluid mechanics problems. 

Check: Best Fluid Mechanics Books That Are Used!

Difference Between Compressible and Incompressible Flows

What is the Incompressible Flow?

In a flow mechanism that a fluid is flowing, if the density of the fluid does not change during the flow, this flow is called an incompressible flow. In incompressible flow mechanisms, fundamental fluid mechanics laws can be used. The most important system that has incompressible flow mechanisms is where room temperature water is used as the fluid. For example, water pumping systems are incompressible flow. 

In theory, there is no incompressible flow in nature. And all the fluid substances’ densities change with the pressure change. But for some fluids, this change is very minimal and they are assumed as incompressible substances. 

Compressible Flow Mechanisms

Instead of incompressible flow mechanisms, in the compressible flow mechanisms, the density of the fluid during the flow changes. COmpressible flow mechanisms are much more complex and the calculations of these mechanisms are different from the incompressible flow mechanisms. 

The most familiar example of the compressible flow is the flow of gasses at different pressures such as jet engine nozzles, gas turbines, etc. Burnt gases are flowing at a very high speed in these systems. The density of the gases is very susceptible to even a very small change of pressure. For example, only the change of 0.01 atm of atmospheric pressure changes the density of the air by 1%. 

Mach Number for Gas Flows

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Mach number is a very critical number for gas flows in the systems where the velocity of the gases is very high. According to the Mach number, fluid flows are characterized. 

In this formula, the speed of flow is divided by the speed of sound in that pressure and atmosphere. For example, the speed of sound in the atmosphere and room temperature is 346 m/s. According to the result of the Mach number of the flow; 

  • Subsonic flow: If the Ma is smaller than 1, the flow is called subsonic flow. 
  • Sonic flow: If the Ma is equal to the 1i the flow is called sonic flow. 
  • Supersonic flow: If the Ma is bigger than the 1, the flow is called supersonic flow. 
  • Hypersonic flow: If the Ma is bigger than 1 by far, the flow is called hypersonic flow.


The use of the Mach number calculator is very simple. You just need to enter the required values; the speed of sound in the flow atmosphere and the speed of flow in your application. Click on the ‘Calculate’ button to see if your application is compressible or incompressible. Click on the ‘Reset’ button to make an other Mach number calculation.

How to Consider Compressible Flows as Incompressible Flows

The fluid mechanic’s calculations for compressible flows are much more accurate than the incompressible flows, and compressible flows are preferred to make calculations. 

From the engineering viewpoint of fluid mechanics, the density changes up to 5% can be assumed to be compressible flow. This nearly equals the Ma = 0.3. If the Mach number of the fluid flow is smaller than 0.3, the fluid flow can be assumed to be a compressible flow in which classical fluid mechanics formulations can be used. 


The general explanation of the compressible and incompressible flows in fluid mechanics can be made like above. We would like to give a general idea of the compressible and incompressible flow assumptions in fluid mechanics applications. 

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

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