Reynolds Number Formula

Reynolds number is a dimensionless value which is used in fluid mechanics to indicate whether the fluid flow in a duct or pat a body is steady or turbulent. This value is determined 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

Formula

The Reynolds number formula is expressed by,

Where,

• 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.

Solved Example

Question: Determine the Reynolds number for a viscous fluid with viscosity of 0.5 Ns/m² relative density 500 Kg/m3 through a 10 mm pipe with a Velocity of 3 m/s.

Solution:

Given: 

μ = 0.5 Ns/m²

ρ = 500 Kg/m3

L = 10 × 10-3 m

V = 3 m/s

The equation of Reynolds is

Re = ρVL / μ

Re  = (500×3×10×10−3)/ 0.5

Re  = 15000 x 10-3 / 0.5

Re = 30

From the figure above, we note that the Reynolds number is less than 2000. Therefore, the flow of fluid is laminar.

 

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