Reynolds number is used to check whether the flow is laminar or turbulent. It is denoted by **R**_{e}. 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 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 R

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

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

Viscosity of fluid $\mu$ = 0.4 Ns/m

Density of fluid $\rho$ = 900 Kg/m

Diameter of the fluid L = 20 $\times$ 10

The Reynold formula is given by R

= $\frac{900 \times 2.5 \times 20 \times 10^{-3}}{0.4}$

= 112.5

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

Given: Diameter of pipe L = 80 mm,

Velocity of the fluid v = 5 m/s,

Density of fluid $\rho$ = 1400 Kg/m

Viscosity of fluid $\mu$ = 0.9 Kg/ms

The Reynolds number is given by R

= $\frac{1400 \times 5 \times 0.08}{0.9}$

= $\frac{560}{0.9}$

= 622.22.

The flow is laminar.