# Reynolds Number

PhysicsFluids

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## Introduction

The ratio of inertial forces is a significant part of this kind of number. Inertial forces, related to viscous forces are relevant in this regard. The formula for calculating the Reynolds number is Reynolds Number = Inertial Force/Viscous Force. This formula is also presented as $\mathrm{R_e \:=\:\rho\: VD/ \mu}$. As per this formula, $\mathrm{R_e}$ is the value of the Reynolds number. The value of density within a fluid is presented by $\mathrm{\rho}$. This equation is important as it also presents the velocity of the flow with the symbol V. D is the indicator of pipe diameter. The viscosity of the fluid is presented with the symbol $\mathrm{\mu}$.

## What is Reynolds's number?

Named after Osborne Reynolds, these numbers are used in measuring fluid flow. The motion of an airplane is a significant part of the identification process of these numbers. Reynolds numbers are an important part that helps to calculate the viscosity and velocity of a fluid and flow (Baidya et al. 2021). In case of a high result, the flow through the pipe is expected to be turbulent. In case of a low result, the flow is expected to be laminar in nature.

Figure 1: Laminar Flow

Based on different ranges, the turbulent and laminar flows are expected to be classified accordingly. In the Reynolds number, the Laminar flow falls under 1100. In case of turbulence, the Reynolds number is fallen under the range of 2200. This range is very important to depict the nature and characteristics of the Reynolds number.

## Characteristics of Reynolds number

The Reynolds number is widely used for determining the nature of fluids. The nature of the fluid can differ from various components. The fluid can be turbulent or laminar in nature. The range of numbers under 2100 is equal to the laminar flow whereas the numbers greater than 2100 are turbulent in nature (Grossmann, Lohse & Sun, 2019). The velocity of the cell centers is also an important part that helps in indicating cell numbers. The components and the nature of Reynolds are dependent on some significant factors. Pressure is one of these factors that impact the overall characteristics of the Reynolds number.

Figure 2: Turbulence Flow

In the case of an ideal gas, the temperature of the surrounding environment and pressure are important. The mainstream velocity and characteristics length are other two important factors that directly impact the Reynolds number. In recent times, Reynolds numbers are widely used. In modeling the significant movements of each different organism that swims through water, the Reynolds number is used. In predicting the formation and transition of laminar form to the turbulent flow, the Reynolds number is widely used (Lee & Moser, 2019). Different kinds of flow situations can be scaled with the help of Reynolds numbers. The main three types of flow are associated with the characteristics of these numbers which are laminar flow, transition flow ad turbulent flow. The Reynolds numbers are also used in maintaining a proper flow that helps in preventing the formation of different biofilm.

## Importance of Reynolds number

The importance of the Reynolds number in terms of fluid flow situations is very high. It has several applications in electrical devices as well as other purposes like electric circuits and other mechanical bodies. The Reynolds number guides to predict the possibility of flow in several types of fluid flow situations of a machinery device (Lee & Moser, 2019). There are 2 principal types of flow that can be seen according to Reynolds’s number laminar flow as well as turbulent flow.

Figure 3: The formula for Reynolds number

In the case of the higher Reynolds number process turbulent dominate the flow and tends that guides to accurately predict the possible pattern of flow in the aspects of fluid flow situations. The Reynolds number is also determined by the rate of different types of internal forces in terms of viscous forces (Saritha, & Banerjee, 2019). In the case of Laminar flow, the Reynolds number is lesser than 1100 while in the case of turbulent flow, the Reynolds number is greater than 2200.

## Application of Reynolds number

The application of this number system guides to include the best possibility of the application in the wind tunnel that guides to study of the various aerodynamic properties of different surfaces (Singh & Frankel, 2020). Another important application in the Reynold number application is very helpful, particularly in terms of supersonic flights with the localized increment in terms of density of the air that surrounds the aircraft.

## Conclusion

In terms of friction factor, the number system is very much applicable. According to the Reynold number, Laminar flow is the very classified type in which the fluid proceeds along with a straight line while in the other flow of fluids the fluid does not move smoothly and the pattern of flow is also mixed with a different direction. Reynolds number has a significant part in terms of calculation of friction factor with a few equations of the fluid machines which also comprises of Darcy-Weisbach equation.

## FAQs

Q1. What are the properties of the Reynolds number?

This number system guides the electric engineers to accurately decides whether the flow is laminar or turbulent. In the case of the lower Reynolds number process, the flow tends to be dominated by the laminar flow.

Q2. What is the formula of the Reynolds number?

$\mathrm{R_e\: = \:\rho VD/ \mu}$ is the formula for the Reynolds number. In this formula $\mathrm{\rho}$ is fluid, V is the flow velocity and D is the diameter of the pipe and $\mathrm{\mu}$ is fluid velocity.

Q3. What is the calculation process of Reynolds number?

The calculation process of Reynolds number includes the multiplication of fluid velocity with pipe diameter. The number is also divided by the value of kinematic viscosity.

Q4. How is Reynolds number helpful?

The application of this number can also be seen in the organism modeling movement that includes swimming through liquid particles like water. Sometimes the atmospheric air is also considered as the fluid then the Reynolds number is very helpful for the calculation process.

Updated on 13-Oct-2022 11:19:47