# The Reynolds Number

The Reynolds number is not only used to characterize the flow patterns, such as laminar or turbulent flow, but also to determine the dynamic similitude between two different flow cases.

The latter is an important concept to ensure valid experimental or computational results of numerous scaled models for industrial applications.

where $\rho $ is the fluid density (kg/m3), $u$ the mean flow velocity (m/s), $L$ the characteristic length (m), for example, hydraulic diameter for internal flows, and $\mu $ the dynamic viscosity of the fluid (kg/(m-s).

where A is the cross-section area (m2) and P is the wetted perimeter (m). The wetted perimeter is the total perimeter of subject walls in contact with the flow.

Fluid flows are laminar when their Reynolds number is below a certain critical value and they are turbulent when they are larger than this critical value, termed the critical Reynolds number (Recr). This critical Reynolds number is between 2,300 and 4,000 for pipe flows.

The critical Reynolds number is also referred to as the transition Reynolds number. It varies widely depending on the conditions of surface roughness, flow disturbances, flow velocity and geometric considerations. For example, the critical Reynolds number for the boundary layer flow over a flat plate reaches about 500,000 based on the free stream velocity outside of the boundary layer and characteristic length of the distance from the leading edge of the plate.