# What is the relation between incompressible flow and laminar flow?

I have a small question about dynamics. My textbook shows me the velocity profile for an incompressible flow, which has a parabolic profile. Does this automatically mean it's laminar flow?

I don't see the relationship in between the two, as laminar flow means the velocity is relatively low whereas incompressible means it's beneath a certain pressure.

Any help is greatly appreciated!

• That's a strange definition of incompressible. Normally I hear "density is constant" as the definition for that. Or more formally, $\partial \rho/\partial p=0$ (cf., my answer here). – Kyle Kanos Feb 4 at 18:28

## 1 Answer

Incompressible flow is found in liquids, which are very resistant to compression. Compressible flow is found in gases, which are easy to compress, and have the pressure-volume relationship given by the gas law of $$PV=znRT$$, where the factor $$z$$ is a compressiblilty factor that accounts for non-idealities.

Laminar flow occurs when the velocity is low, both for liquids and gases. This flow is recognized by the parabolic flow profile for fluid flow through pipes, and it occurs at low Reynolds numbers. See https://en.wikipedia.org/wiki/Reynolds_number for much more detail.

If the velocity and Reynolds number get sufficiently high, the flow changes to turbulent flow, which is characterized by high frequency random fluctuations across the cross-sectional area of the flow stream, and the whole flow stream has a cross-sectional flow profile that is approximately the same, except at the pipe walls.

Both compressible flow and incompressible flow can be in the laminar flow range, the turbulent flow range, or a transition flow range, where the flow is changing from laminar to turbulent. Thus, the terms "incompressible" and "laminar" are describing two distinctly different physical phenomena.