Reynolds Number Formula

Reynolds number is a dimensionless value which is applied in fluid mechanics to represent whether the fluid flow in a duct or pat a body is steady or turbulent. This value is obtained by comparing the inertial force with the viscous force.

The Reynolds number id denoted by Re.

Reynolds number is given by

Reynolds Number = Inertial Force / Viscous Force

The Reynolds number formula is expressed by,

\(\begin{array}{l}R_{e} = \frac{\rho VL}{\mu }\end{array} \)


ρ = Fluid density

V = Fluid velocity

μ = Fluid viscosity

L = length or diameter of the fluid.

Reynolds number formula is used to determine the velocity, diameter and viscosity of the fluid.

The Kind of flow is based on the value of Re

  1. If Re < 2000, the flow is called Laminar
  2. If Re > 4000, the flow is called turbulent
  3. If 2000 < Re < 4000, the flow is called transition.

Example 1

Calculate the Reynolds number if a liquid of viscosity 0.5 Ns/m2 and relative density of 500 Kg/m3 through a 10 mm pipe flows with a Velocity of 3 m/s.



μ = 0.5 Ns/m2

ρ = 500 Kg/m3

L = 10 × 10-3 m

V = 3 m/s

The Reynolds formula is

Re = ρVL / μ

Re = (500×3×10×10−3)/ 0.5

R= 15000 x 10-3 / 0.5

R= 30

Here, we notice that the value of Reynolds number is less than 2000, therefore the flow of liquid is laminar.


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  1. So, when do we have to consider on Re whether it is Tuburlent or Laminar ? Before we directly do the exercises ?