# Reynolds Number Formula

## What is Reynolds Number?

Reynolds Number is basically the ratio of the internal forces to the viscous forces in a fluid. This ratio depends on several factors, such as the internal motion due to different fluid velocities. The Reynolds Number is an important number in mechanics and is a dimensionless quantity, i.e. it had no units. The Reynolds Number has several applications, we shall discuss the applications as we progress further. Its primary application is the prediction of change from laminar to turbulent flow.

### A Sneak Peek into The History

The concept of Reynolds number, internal forces, viscous forces was introduced by George Stokes back in the year 1851. However, there was no solid theory behind it. The idea was further polished and built upon in the year 1908 by Arnold Sommerfeld. The name Reynold comes from Osborne Reynolds, the man who popularized the use of Reynolds Number in the year 1883.

### The Formula for Reynolds Number

The formula for Reynolds Number is as given below

Re = $\frac{\rho u L}{\mu}$ = $\frac{u L}{\nu}$

In the formula given above,

ρ Is rho or the density of the given fluid.

u is the speed with which the fluid flows

μ is the dynamic viscosity of the fluid.

L is the characteristic linear dimension.

V is the kinematic velocity of the given fluid.

### The Significance of Reynolds Number

So now that you've learned the formula of the Reynolds Number and who exactly formulated the Reynolds Number and in what year, you must be wondering what does this mere number signify. Well, the Reynolds Number signifies the nature of the flow of a fluid across a cross-section. On a wide basis, there are two types of flowing styles that a liquid can flow in. One is laminar flow and the other is turbulent flow. Reynolds number is used to determine the type of flow of a fluid.

If Reynolds Number < 2300, then the liquid follows the laminar flow

If Reynolds number >2900, the liquid follows the turbulent flow

1. What is the type of flow when the Reynolds Number lies between 2300 and 2900?

This is the confusing range of Reynolds numbers. It is the range where it is difficult to determine the type of flow. It is the range where the type of flow is transiting from laminar to turbulent. In this range of Reynolds number, the flow could either be laminar or turbulent. It isn't easy to determine. It depends on factors like the surface through which the fluid is flowing. The flow could at times be laminar and at times be turbulent. The flow in this range is dynamic and could switch types from time to time. Hence, it's called intermittent flow.

2. What does Reynolds Number depend on?

Reynolds number depends upon several factors. The factors on which the Reynolds Number depends on are

• The density of the fluid: the density plays a key role in determining several physical factors of a fluid. Density is hence one of the primary factors that determine Reynolds Number.

• The speed with which the liquid is flowing in the cross-sectional area.

• Mu or the dynamic viscosity constant of the fluid.

• L, the length of the linear cross-section of the pipe.

3. What are the applications of Reynolds number?

The Reynolds Number does have several practical applications in the real-time world! The Reynolds Number's primary application is the analysis of the flow of a fluid in a cross-sectional area. It helps determine the velocity at which the flow transits from laminar to turbulent. The Reynolds Number is applied in determining the behaviors of different liquids. For instance, the movement of glycerine is predicted in a circular duct. The Reynolds Number is observed to be below 2300, hence we can conclude that the flow is laminar!