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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,

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.

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:

μ = 0.5 Ns/m2

ρ = 500 Kg/m3

L = 10 × 10^-3 m

V = 3 m/s

The Reynolds formula is

R_e = ρVL / μ

R_e = (500×3×10×10⁻³)/ 0.5

R_e = 15000 x 10^-3 / 0.5

R_e = 30

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