The critical Reynolds number  is a dimensionless parameter used in fluid mechanics to determine the transition from laminar to turbulent flow in a pipe or over a body. The critical Reynolds number varies depending on the geometry and flow conditions, and it marks the point at which the flow becomes unstable and transitions from smooth, orderly motion (laminar flow) to chaotic, irregular motion (turbulent flow). This equation provides an estimate of the Reynolds number at which the transition from laminar to turbulent flow occurs. ​The critical Reynolds number equation is typically given as,

Where:

• Re crit​ is the critical Reynolds number.
• $R$ is the surface roughness of the pipe or body.
• $D$ is the characteristic hydraulic diameter of the flow.