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# Reynolds Number Formula

Reynolds number is used to check whether the flow is laminar or turbulent. It is denoted by Re. This number got by comparing inertial force with Viscous force. Reynolds number formula is given by Where,
$\rho$ is the density of the fluid,
V is the velocity of the fluid,
$\rho$ is the density of fluid,
$\mu$ is the viscosity of fluid,
L is the length or diameter of the fluid.

Reynolds number formula is used in the problems to find the Velocity (V), density ($\rho$), Viscosity ($\mu$) and diameter (L) of the fluid. It is dimensionless.

The Kind of flow depends on value of Re
1. If Re < 2000 the flow is Laminar
2. If Re > 4000 the flow is turbulent
3. If 2000 < Re < 4000 it is called transition flow.

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## Reynolds Number Problems

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Below are  problems based on Reynolds number which may be helpful for you.

### Solved Examples

Question 1: Find the reynolds number if a fluid of viscosity 0.4 Ns/m2 and relative density of 900 Kg/m3 through a 20 mm pipe with a Velocity of 2.5 m/s?
Solution:

Viscosity of fluid $\mu$ = 0.4 Ns/m2,
Density of fluid $\rho$ = 900 Kg/m3,
Diameter of the fluid L = 20 $\times$ 10-3 m

The Reynold formula is given by Re = $\frac{\rho V L}{\mu}$
= $\frac{900 \times 2.5 \times 20 \times 10^{-3}}{0.4}$
= 112.5
Here we observe that the value of Reynolds number is less than 2000, so the flow of liquid is laminar.

Question 2: Calculate the reynolds number if a fluid flows through a diameter of 80 mm with velocity 5 m/s having density of 1400 Kg/m3 and having viscosity of 0.9 Kg/ms.
Solution:

Given: Diameter of pipe L = 80 mm,
Velocity of the fluid v = 5 m/s,
Density of fluid $\rho$ = 1400 Kg/m3,
Viscosity of fluid $\mu$ = 0.9 Kg/ms
The Reynolds number is given by Re = $\frac{\rho V L}{\mu}$
= $\frac{1400 \times 5 \times 0.08}{0.9}$
= $\frac{560}{0.9}$
= 622.22.
The flow is laminar.

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