**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,

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

- If Re < 2000, the flow is called Laminar
- If Re > 4000, the flow is called turbulent
- 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.