Reynolds number

Introduction

When the liquid flows through the pipe, it will hit the line. The prominent role of the engineer is to make sure that the fluid flows through the tube throughout the surface steadily. Therefore, for such concern, a number known as Reynolds number is used that helps to predict whether the flow of liquid is steady or turbulent. In this article, we will discuss the importance of the Reynolds number and also provide some examples of finding the value of the Reynolds number.

The concept of Reynolds number was initially being introduced by Sir George and later got popular by Osborne Reynolds, and finally, such a number is known to be Reynolds number. In general words, we can say that the Reynolds number is a pure number that helps to determine the flow of liquid through the pipe.

 The critical velocity vₙ is denoted by 

 vₙ = Nᵣη/ρD 

Or Nᵣ = ρDvₙ/η

Where η determine the coefficient of viscosity of the liquid flowing through the tube

Where ρ = density of the liquid

Nᵣ = It is a constant called as a Reynolds number

Here, vₙ is the critical velocity.

Reynolds number units  

• Unit of Reynolds Number = (kg/m 3) x (m/s) x m / (kg/m.s)
• Reynolds Number units = kg x m x m x m.s/ (m 3 x s x kg)
• Unit of Reynolds Number = 1 = no unit

Points to be Remember

We need to know that the average speed of the fluid is not identical at all places available in the pipe, which indicates that the speed of the fluid is maximum, however at surfaces, speed will be less means closer to zero .

Importance of Reynolds number in Heat Transfer

Some of the major significance of Reynolds number in the heat transfer are listed below

1. The value of Reynolds number helps to determine the relationship between the viscous force and inertia forces in the flow of liquid.

2. Concerning the Reynolds number value, we will be able to determine the flow of liquid i.e.

• If Re < 2300, then the flow of liquid is laminar.

• If 2300 < Re < 3500, then the flow of liquid  is transient.

• If Re > 3500, then the flow of liquid is turbulent.

3. Reynolds number is employed in the connective heat transfer for the criteria of dynamics and kinematics similarity. 

Critical Velocity

Critical velocity is the velocity up to which the  liquid flow is laminar or streamlined, and above which liquid flow seems to become turbulent. The critical velocity of the liquid flow is denoted by

 vₙ = Nᵣη/ρD 

To make liquid flow streamlined, the value of critical velocity should be larger, however for η, the value needs to be smaller.

Reynolds Number- Derivation

We can define Reynolds number as the ratio of the inertial forces classified to the viscous force per unit area of the flowing fluid.

Let us take an example! Take a tube having the small area of the cross-section A from which fluid flows with velocity and has density ρ.

Now, we will carry out the derivation of the Reynolds number 

Liquid mass through tube per second, 

∆m = volume of fluid flowing per second x density of the fluid.                     

 = A v x ρ

 Inertial force per unit area  will be equal to the rate of change of area .

= (∆m)v/A = (A v x ρ)v/A = v2ρ…(1)

viscous force, F = ηAv/r

∵ Viscous force per unit area = F/A = ηv/r….(2)

By dividing the equation 1 by equation 2 , we get the below result      

Nᵣ = v2ρ/ ηv/r = vρr/η       

Point to remember: The Reynold number is independent of the units 

Understanding the value of Reynolds Number

If the calculated value of the Reynolds number is more than 2000, it can be said that the flow of the pipe will be turbulent, however if the value is less than 2000, flow will be laminar. In numerical terms, such values are accepted , but generally turbulent and laminar are determined on the basis of range. The laminar flow comes under the value of 1100 and turbulent flow  comes under the range of above 2200 value. 

Reynolds Number Calculation Example

We will take an example to calculate the Reynolds number value

• Let us suppose that water at 5m/s flows through the pipe having a diameter of 25mm. The dynamic viscosity of the water is found to be 0.001 Pa.s. determine whether the flow of water is in transition state or laminar state ?

Solution:-

Given 

Diameter( D) = 25mm

Water dynamic viscosity ( μ) = 0.001 Pa.s= 0.001 N.s/m²

Velocity (v)=5 m/s=0.5 m/s

Reynolds number is give by

Re=ρvD/ μ

Putting the value in the above formula of Reynolds number

=1000× 0.6×0.025/ 0.001

1000×0.6×0.025/ 0.001

On solving the above expression we will get value of Reynolds number 

Re = 12500

As Re> 3500, therefore flow of water is said to be turbulent 

Conclusion

We have discussed Reynolds number in detail to make students learn about the importance of Reynolds number by reviewing the study material along with examples of calculating the value of Reynolds number and determining the flow of liquid.