# What is Reynolds number? How to classify laminar and turbulent flow based on Reynolds number?

What is Reynolds number? How to classify laminar and turbulent flow based on Reynolds number?

Reynolds number is the ratio of inertial force to viscous force. A boundary layer is a layer where the behavior of these forces get change.\[Re = \frac{{\rho VL}}{\mu } = \frac{{VL}}{\nu }\] Here, \(\rho \) is the density, \(V\) is the flow speed, \(L\) is the characteristic linear dimension, \(\mu\) is the dynamic viscosity of the fluid, and \(\nu\) is the kinematic viscosity of the fluid.

Laminar flows are smooth flow. It occurs at low Reynolds numbers. Here viscous forces are dominant. Turbulent flows have chaotic eddies, there are vortices, and inflow instabilities. They have a higher Reynolds number. There is a transition from a laminar flow to turbulent flow in a flow field and the Reynolds number at which it occurs is known as a critical Reynolds number. Reynolds number is also used to manage the scaling effect. For example, an airfoil in a wind tunnel test is small as compared to its original size in wings of the aircraft. Matching their Reynolds number is required to get a similar characteristics.

Flows over geometrical similar bodies having same Reynolds and Mach number are dynamic similar, and lift, drag and moment coefficients for these bodies will be identical.