# 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,

$R_{e}\,&space;=\,&space;\frac{\rho&space;VL}{\mu&space;}$

Where,

ρ = density of the fluid,

V = velocity of the fluid,

μ = viscosity of fluid,

L = length or diameter of the fluid.

Reynolds number formula can be used in the problems to calculate the Velocity (V), density (ρ), Viscosity (μ) and diameter (L) of the liquid.

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.

Solution

Given:

Viscosity of fluid, μ = 0.5 Ns/m2,

Density of fluid, ρ = 500 Kg/m3,

Diameter of the fluid, L = 10 × 10-3 m

The Reynolds formula is given by,

Re = ρVL / μ

= 500×3×10×10−3 / 0.5

= 15000 x 10-3 / 0.5

= 30

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

Example 2

Determine the Reynolds number if a liquid flows through a diameter of 50 mm with velocity 5 m/s having density of 1500 Kg/m3 and viscosity of 0.9 Kg/ms.

Solution:

Given:

Diameter of pipe L = 50 mm,

Velocity of the fluid v = 5 m/s,

Density of fluid ρ = 1500 Kg/m3,

Viscosity of fluid μ = 0.9 Kg/ms

The Reynolds number is given by

Re = ρVL / μ

= 1500×5×0.050 / 0.9

= 416.66

Hence, the flow is laminar.