### Reynolds Number - Instrumentation Engineering

#
REYNOLDS NUMBER

**Reynolds number**is a ratio of the inertial force to the viscous force in a fluid flow. Irish innovator

**first noticed this ratio. The Reynolds number is used to determine whether a fluid is laminar or turbulent. It is dependent upon the viscosity of a fluid. So we can determine the Reynolds number in some different cases.**

*Osborne Reynolds*Osborne Reynolds |

### CASE I: No Viscosity is Present

Flow profile moves parallel if there is no viscosity and there
will be no distortion in the flow profile. It will move straight, it means the
flow profile will be rectilinear.

**F**

_{B }= F_{I }– F_{V max}
F

_{C }= F_{I}### CASE II: Viscosity is Present

There is a viscous force, acting on the particle in the
opposite direction of the movement of the particle.

Here we get

**parabolic profile**when its –**(i)**

**Viscosity is low**

**(ii)**

**Absolute viscosity is high**

Parabolic profile is also known as

**Laminar flow profile**.### CASE III: Viscosity is in between zero and Absolute viscosity (A.V) [0<viscosity<A.V]

When the velocity is high the viscosity will be low and vice
versa. Here these profile are called as Turbulent flow profile.

Here we get

**turbulent profile**when its –**(i)**

**Velocity is very high**

**(ii)**

**Viscosity is very low**

## FORMULA

**Reynolds number = Internal force / Viscous force**

R

_{N}= F_{I}/ F_{r}_{}

**R**

_{N }= (ρvD)/µ

Where, ρ = Density of the fluid

v = Average
velocity of the fluid

D = pipeline
diameter

µ = Absolute
viscosity

## Reynolds number and Flow profile

If,

**R**= Flow profile is

_{N}< 2000**laminar**

**R**= flow profile is

_{N}> 4000**turbulent**

If, the

**Reynolds number**of the fluid is between 2000 and 4000, the flow profile is a complex mixture of laminar flow and turbulent flow, which is called**Transition region**. In this state we can’t use any flow meter.## CONCLUSION

For industrial purpose R

_{N }is made above 10,000.
If we assume that the fluid has no viscous force ( F

_{r }), then
F

_{r }= 0
So, Reynolds number, R

_{N }= F_{I}/ F_{r}_{}

So,

**R**_{N }= infinite**(∞)**

Then it is known as

**Rectilinear flow profile**.
It means, the turbulent flow profile is in between the
rectilinear and the laminar flow profile.

**Read Also,**

**Specific Gravity of Fluid : http://www.theincredibletruths.com/2018/09/specific-gravity-industrial.html**

**RTD Wiring : http://www.theincredibletruths.com/2018/08/rtd-wiring-color-code.html**

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