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Introduction:

If we understand and Calculate Reynolds Number Formula then we can easily understand the mechanism flow. Reynold Number formula regulates how fluid flows. The behavior of fluid depends upon Fluid Mechanics. Fluid mechanics is the branch of Physics which actually deal with how fluid flows in various medium.

This Fluid mechanism could be understood through a formula which is called as a “Newtonian Fluid Reynolds Number Formula”. It is often called as “Reynolds Number Formula.”

#### Reynolds Number Formula:

Reynolds Number could be calculated using the ratio of “Inertial Force” and “Viscous Force”. It could be written as:

Reynolds number = (Inertial Force / Viscous Force)

It would be demonstrated as:

How to calculate the Reynolds Number Formula

Where,

ρ \=> Fluid Density,

V => Fluid Velocity,

μ => Fluid Viscosity,

D or (L) => Length or diameter of the fluid.

#### How to Understand the Formula composition:

Fluid Density and Fluid Velocity are directly proportional to the Reynold Number. Fluid Viscosity is inversely proportional to Reynold Number. It is used to find the velocity, diameter and viscosity of the fluid in any specific environment.

#### Different Kind of flows:

There are 3 kinds of flows, based on the Reynold Number:

1. Laminar
2. Transitions
3. Turbulent

We would understand each with respect to the Reynold number. Reynold number would decide the flows:

1.If Re < 2000 then flow is called as “Laminar”,

2.If Re > 4000 then flow is called as “Turbulent”,

3.But if Re number is between 2000 and 4000 (2000 < Re < 4000) then it is called as “Transition”.

One can easily find the type of flows using above Reynold number.

Let’s understand through example.

#### Example1:

Q1. The liquid has viscosity of 0.6Ns/m2 and their relative density is 600Kg/m3. If this liquid passes through a 10 mm pipe with a velocity of 2 m/s. Calculate the Reynolds Number ?

Given:

μ = 0.6 Ns/m2

ρ = 600 Kg/m3

L = 10 × 10-3 m

V = 2 m/s

Solve using

Re = ρVL / μ

Re = (600×2×10×10−3)/ 0.6

= 12000 x 10-3 / 0.6

Re = 20

Observation:

We can observe that Reynold Number (Re ) is less than 2000 so flow is “Laminar”

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#### Example2:

Q2. The liquid has viscosity of 0.7Ns/m2 and density is 70000Kg/m3. If this liquid flows with the velocity of 3.5 m/s through a 10 mm pipe. Find the Reynolds Number ?

Given:

ρ = 70000 Kg/m3

μ = 0.7 Ns/m2

V = 3.5 m/s

L = 10 × 10-3 m

The Reynolds formula is

Re = (ρVL / μ)

Re = (70000×3.5×10×10−3)/ 0.7

\= 2450 / 0.7

Re = 3500

Observation:

Here, we can observe that Reynold Number is greater than 2000 but less than 4000 so it would observe the flow of “Transitions”.

Let’s just assume you got the Reynold number more than 4000 then flow would be considered it as “Turbulent”.

Above two examples we understand and calculate Reynold Number Formula.

One can explore more details about Reynold Number Formula using the below links:

https://en.wikipedia.org/wiki/Reynolds_number#Definition

https://en.wikipedia.org/wiki/Reynolds_number#History

https://en.wikipedia.org/wiki/Reynolds_number

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