### Reynolds Number

• Calculate Reynold’s Number and understand its significance.

• Define a flow as laminar, turbulent or transition based on Reynolds Number.

It is the ratio of inertia force to the viscous force. i.e.

$Re =\dfrac{vD\rho }{\mu } = \dfrac{vD}{\nu }$

Re = Reynold’s Number,
D= Diameter of pipe,
v= Mean velocity
$\mu$ = Dynamic viscosity,
$\nu$ =Kinematics viscosity of flow,
$\rho$ = Fluid density
It has been found that for flow in circular pipes the critical Reynold’s number is about 2000. At this point the laminar flow changes to turbulent flow. The transition from laminar to turbulent does not exactly happen at Re=2000 but varies from one experiments to another experiments due to experimental condition.

### Solved Example:

#### 63-1-01

For pipes, laminar flow occurs when Reynold's number is: (HPCL Asst Maintenance Mech 2019)

Solution:
Laminar flow generally occurs when the Reynolds number is less than 2000. Turbulent flow occurs at an Re above 4000 and transitional flow occurs between 2000 and 4000.

### Solved Example:

#### 63-1-02

A large Reynold's number is indication of: (ISRO IPRC Tech Asst Mech Aug 2016)

Solution:
Reynold's number indicate whether the flow is laminar or turbulent. It is the ratio of inertial forces to viscous forces. At higher Reynold's number, inertial forces are dominant as compared to viscous forces, which indicate the flow is highly turbulent.

### Solved Example:

#### 63-1-03

For pipes, turbulent flow occurs when Reynolds number is:

### Solved Example:

#### 63-1-04

Reynold's number is significant in:

### Solved Example:

#### 63-1-05

The velocity at which the laminar flow stops is known as: (ISRO Scientist ME 2015)

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number $Re_D$ = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is: (GATE ME 2019)