# Reynold’s Number

## Reynold’s Number

The Reynold’s number is named after the British Physicist Osborne Reynold’s. He discovered this while observing different fluid flow characteristics like flow of a liquid through a pies and motion of an airplane wing through the air. He also observed that the type of flow can transition from laminar to turbulent quite suddenly.

What is Reynold’s Number?

Reynold’s Number which referred to Re. Reynold’s Number is a dimensionless quantity which is used in fluid mechanics to predict the flow of patterns in different fluid flow conditions. The Reynold’s Number is the ratio of a fluid’s inertial force to its viscous force. Inertial force involves force due to the momentum of the mass of flowing fluid. Viscous forces deal with the friction of a flowing fluid.

The mathematical representation is:

$${{R}_{e}}=\frac{\rho uL}{\mu }=\frac{uL}{\nu }$$.

Where,

ρ = Density of the fluid,

μ = Dynamic viscosity of the fluid,

v = Kinematic viscosity of the fluid,

L = Characteristic linear dimension,

u = Velocity of the fluid with respect to the object.

Using Reynolds Number it becomes easy to determine whether the fluid flow is laminar or turbulent. Below are the boundary values of a circular pipe that can be used to determine the flow pattern:

If 2300 < Re < 4000, then the flow is said to be transient.

If Re > 2300, then the flow is said to be laminar.

If Re > 4000, then the flow is said to be turbulent.

Laminar flow is the type of flow in which the fluid travels smoothly in regular paths. Conversely, turbulent flow is not smooth and follows an irregular maths with lots of mixing.

Reynold’s Number comprises both static and kinematic properties of fluids, it is specified as a flow property since dynamic conditions are investigated.