# What is Critical Reynolds Number – Definition

The critical Reynolds number is associated with the laminar-turbulent transition, in which a laminar flow becomes turbulent. Critical Reynolds Number

## Critical Reynolds Number The Reynolds number is the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent.

The critical Reynolds number is associated with the laminar-turbulent transition, in which a laminar flow becomes turbulent. This is an extraordinarily complicated process, which at present is not fully understood.

## Critical Reynolds Number for Flow in a Pipe

For flow in a pipe of diameter D, experimental observations show that for “fully developed” flow, the critical Reynolds number is about Red,crit = 2300.

• Laminar flow. For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. The accepted transition Reynolds number for flow in a circular pipe is Red,crit = 2300.
• Transitional flow. At Reynolds numbers between about 2000 and 4000 the flow is unstable as a result of the onset of turbulence. These flows are sometimes referred to as transitional flows.
• Turbulent flow. If the Reynolds number is greater than 3500, the flow is turbulent.

Note that, the critical Reynolds number is different for every geometry.

## Critical Reynolds Number in boundary layer flow over a flat plate.

In determining whether the boundary layer is laminar or turbulent, it is frequently reasonable to assume that transition begins at some location xcrit, as shown in figure. This location is determined by the critical Reynolds number, Rex,crit. For flow over a flat plate,
transition from laminar to turbulent boundary layer occurs when Reynolds number at x exceeds Rex,crit ~ 500,000. Transition may occur earlier, but it is dependent especially on the surface roughness. The turbulent boundary layer thickens more rapidly than the laminar boundary layer as a result of increased shear stress at the body surface.

## Example: Critical Reynolds Number

A long thin flat plate is placed parallel to a 1 m/s stream of water at 20°C. Assume that kinematic viscosity of water at 20°C is equal to 1×10-6 m2/s.

At what distance x from the leading edge will be the transition from laminar to turbulent boundary layer (i.e. find Rex ~ 500,000).

Solution:

In order to locate the transition from laminar to turbulent boundary layer, we have to find x at which Rex ~ 500,000.

x = 500 000 x 1×10-6 [m2/s] / 1 [m/s] = 0.5 m

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