Reynolds number equation


For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for the flow in a duct or pipe can with the hydraulic diameter be expressed as. The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is. In practice laminar flow is only actual for viscous fluids - like crude oil, fuel oil and other oils. A Newtonian fluid with a dynamic or absolute viscosity of 0. This calculator can be used if density and absolute dynamic viscosity of the fluid is known.

The calculator is valid for incompressible flow - flow with fluids or gases without compression - as typical for air flows in HVAC systems or similar. The calculator is generic and can be used for metric and imperial units as long as the use of units are consistent. Hydraulic diameter - d h - or c haracteristic length - L m, ft. Default values are for air at 60 o F2 atm pressure and density 0. Dynamic absolute viscosity is 1. The calculator below can be used when kinematic viscosity of the fluid is known.

Default values are for water at 20 o C with kinematic viscosity 1. The characteristic length or hydraulic diameter of the pipe is 0. Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro.

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AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. Make Shortcut to Home Screen?The Reynolds number Re helps predict flow patterns in different fluid flow situations.

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At low Reynolds numbers, flows tend to be dominated by laminar sheet-like flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow eddy currents. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation.

Reynolds numbers are an important dimensionless quantity in fluid mechanics. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow, and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full size version.

The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behaviour on a larger scale, such as in local or global air or water movement and thereby the associated meteorological and climatological effects. The concept was introduced by George Stokes in[2] but the Reynolds number was named by Arnold Sommerfeld in [3] after Osborne Reynolds —who popularized its use in The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.

A region where these forces change behavior is known as a boundary layersuch as the bounding surface in the interior of a pipe. A similar effect is created by the introduction of a stream of high-velocity fluid into a low-velocity fluid, such as the hot gases emitted from a flame in air.

This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which tends to inhibit turbulence. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation.

This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full-size version. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed.

With respect to laminar and turbulent flow regimes:. The Reynolds number is defined as [3]. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. For aircraft or ships, the length or width can be used. For flow in a pipe, or for a sphere moving in a fluid, the internal diameter is generally used today.

Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluidsspecial rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels. In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude.

Fluid flow is generally chaotic, and very small changes to shape and surface roughness of bounding surfaces can result in very different flows. Nevertheless, Reynolds numbers are a very important guide and are widely used.

Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow. In his paper Reynolds described the transition from laminar to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow velocities using a small stream of dyed water introduced into the centre of clear water flow in a larger pipe.

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The larger pipe was glass so the behaviour of the layer of the dyed stream could be observed, and at the end of this pipe there was a flow control valve used to vary the water velocity inside the tube. When the velocity was low, the dyed layer remained distinct through the entire length of the large tube. When the velocity was increased, the layer broke up at a given point and diffused throughout the fluid's cross-section. The point at which this happened was the transition point from laminar to turbulent flow.

From these experiments came the dimensionless Reynolds number for dynamic similarity—the ratio of inertial forces to viscous forces. Reynolds also proposed what is now known as the Reynolds-averaging of turbulent flows, where quantities such as velocity are expressed as the sum of mean and fluctuating components.

Such averaging allows for 'bulk' description of turbulent flow, for example using the Reynolds-averaged Navier—Stokes equations. For flow in a pipe or tube, the Reynolds number is generally defined as [8].

For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the characteristic dimension for internal-flow situations is taken to be the hydraulic diameterD Hdefined as.An increasing Reynolds number indicates an increasing turbulence of flow. It is defined as:. This is an extraordinarily complicated process, which at present is not fully understood.

The Reynolds number is the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It can be interpreted that when the viscous forces are dominant slow flow, low Re they are sufficient enough to keep all the fluid particles in line, then the flow is laminar.

Even very low Re indicates viscous creeping motion, where inertia effects are negligible. When the inertial forces dominate over the viscous forces when the fluid is flowing faster and Re is larger then the flow is turbulent. It is a dimensionless number comprised of the physical characteristics of the flow. All fluid flow is classified into one of two broad categories or regimes. These two flow regimes are:. This is a basic classification. All of the fluid flow equations e.

Solution of multi-phase fluid flow is very complex and difficult and therefore it is usually in advanced courses of fluid dynamics. Another usually more common classification of flow regimes is according to the shape and type of streamlines. All fluid flow is classified into one of two broad categories. The fluid flow can be either laminar or turbulent and therefore these two categories are:.

Laminar flow is characterized by smooth or in regular paths of particles of the fluid. Therefore the laminar flow is also referred to as streamline or viscous flow.

In contrast to laminar flow, turbulent flow is characterized by the irregular movement of particles of the fluid. The turbulent fluid does not flow in parallel layers, the lateral mixing is very high, and there is a disruption between the layers.

Most industrial flowsespecially those in nuclear engineering are turbulent. The flow regime can be also classified according to the geometry of a conduit or flow area. From this point of view, we distinguish:. Internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of behaviour of internal flow regimes is of importance in engineeringbecause circular pipes can withstand high pressures and hence are used to convey liquids. On the other hand, external flow is such a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces.

Detailed knowledge of behaviour of external flow regimes is of importance especially in aeronautics and aerodynamics. Laminar flow. For practical purposes, if the Reynolds number is less thanthe flow is laminar. Transitional flow.As an object moves through the atmosphere, the gas molecules of the atmosphere near the object are disturbed and move around the object.

reynolds number equation

Aerodynamic forces are generated between the gas and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the gas going by the object and on two other important properties of the gas; the viscosityor stickiness, of the gas and the compressibilityor springiness, of the gas.

To properly model these effects, aerodynamicists use similarity parameters which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled.

Representative values for the properties of air are given on another page, but the actual value of the parameter depends on the state of the gas and on the altitude.

Aerodynamic forces depend in a complex way on the viscosity of the gas. As an object moves through a gas, the gas molecules stick to the surface. This creates a layer of air near the surface, called a boundary layerwhich, in effect, changes the shape of the object.

The flow of gas reacts to the edge of the boundary layer as if it was the physical surface of the object. To make things more confusing, the boundary layer may separate from the body and create an effective shape much different from the physical shape. And to make it even more confusing, the flow conditions in and near the boundary layer are often unsteady changing in time.

The boundary layer is very important in determining the drag of an object. To determine and predict these conditions, aerodynamicists rely on wind tunnel testing and very sophisticated computer analysis. The important similarity parameter for viscosity is the Reynolds number. The Reynolds number expresses the ratio of inertial resistant to change or motion forces to viscous heavy and gluey forces. The Reynolds number Re then becomes:.

reynolds number equation

The gradient of the velocity is proportional to the velocity divided by a length scale L. Similarly, the second derivative of the velocity is proportional to the velocity divided by the square of the length scale.

Reynolds Number

The Reynolds number is a dimensionless number. High values of the parameter on the order of 10 million indicate that viscous forces are small and the flow is essentially inviscid. The Euler equations can then be used to model the flow. Low values of the parameter on the order of 1 hundred indicate that viscous forces must be considered. The Reynolds number can be further simplified if we use the kinematic viscosity nu that is euqal to the dynamic viscosity divided by the density:. Here's a JavaScript program to calculate the coefficient of viscosity and the Reynolds number for different altitude, length, and speed.

The applets are slowly being updated, but it is a lengthy process. This page shows an interactive Java applet which calculates the viscosity coefficient and the Reynolds number for an input velocity, length, and altitude. To change input values, click on the input box black on whitebackspace over the input value, type in your new value, and hit the Enter key on the keyboard this sends your new value to the program.

You will see the output boxes yellow on black change value. You can use either Imperial or Metric units and you can input either the Mach number or the speed by using the menu buttons.With our Reynolds number calculator, you can quickly compute Reynolds number that helps predict whether the flow of a liquid will be laminar or turbulent.

This factor measures the ratio of inertial forces to viscous forces occurring during the fluid movement. Keep reading if you want to find the answers to the questions:. The Reynolds number has broad applications in real life.

Reynolds Number Calculator

It can describe liquid flow in a pipe, flow around airfoils or an object moving in a fluid. In the following text, we have provided Reynolds number equation, units discussion and comparison of laminar and turbulent flows. Read on to find out what are laminar flow and turbulent flow Reynolds numbers. You will also find some examples of calculations which can be done with Reynolds number formula using this calculator.

Are you interested in fluid mechanics? You should also check our buoyancy calculator or Bernoulli equation calculator. They can be very useful in analyzing fluid motion.

Reynolds Number: Equation for Reynolds Number (With PDF)

Reynolds number is one of the characteristic numbers used in fluid dynamics to describe a character of the flow.

For example, if you want to compare a small-scale model e. The Reynolds number is the ratio of inertial forces to viscous forces exerted on a fluid which is in relative motion to a surface. On one hand, inertial forces generate fluid friction which is a factor in developing turbulent flow. On the other hand, viscous forces counteract this effect and progressively inhibit turbulence. The Reynolds number definition generally includes the velocity of a fluid, the characteristic length or characteristic dimension and the properties of the fluid, such as density and viscosity.

If you want to learn more about fluid viscosityyou should check out Stokes' law calculatorwhere you can find, among others, viscosity definition. Although the Reynolds number can be defined in several different ways, it remains a non-dimensional factor. Now, you probably want to know what Reynolds number means at all. Reynolds number is used to predict whether the fluid flow will be laminar or turbulent.

In this situation, the flow will begin to change from laminar to turbulent flow and then back to laminar flow.

It is so-called intermittent or transitional flow. Therefore, the choice of laminar vs turbulent flow isn't always easy and possible. The Reynolds number formula depends on viscosity.The Reynolds number Re is a dimensionless quantity that is used to determine what type of fluid flow to expect in a given situation.

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It is an important tool for engineers who are engaged in fluid mechanicsas it can predict the flow patterns to be expected and help in the modification or optimization of the subsequent designs so as to improve the flow. It can be applied in any kind of flow, from pipes and tubes to completely open channels as the main elements that determine the Reynolds number value are the inertial and the viscous forces of the flowing fluid.

That said, and in order to be able to determine the Reynolds number value, we first need to determine the fluid velocity, density, viscosityand the pipe or channel diameter. When the Reynolds number must be determined for wide ducts or open channels like rivers, we may consider the cross-sectional area A as the semicircle that is formed between the river banks and the river bed.

The corresponding consideration must be made for the hydraulic diameter as well, since the wetted perimeter is determined by the river depth and distance between the two banks. There are two types of flows, namely the laminar and the turbulent, while there also is an identifiable transition phase between these two that holds its own significance for practical reasons.

The laminar flow is a fluid flow that occurs in laminas or layers that slip smoothly upon the adjacent laminas and layers, exchanging kinetic momentum on the molecular level.

Understandig Viscosity and Viscous Force

In the case of the laminar flow, the viscous forces of the fluid help to keep the instability and tendency for turbulence under control. The reasons why we care about whether a fluid flow is turbulent or laminar and why we take action to accommodate the latter are the following:. In practice, the Reynolds number is a simple indication of what to expect, but it should never be taken as a fact since the inner surface of pipes, etc. Even the slightest and smallest serration in a pipe or wall will cause significant changes in the flow of the fluid, so the Reynolds number should only be taken into account with the inclusion of a large safety factor.

Experiments have shown that in general, Reynolds number values between and is the range of transition from laminar to turbulent flow.

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However, it is important to note that the value of the number where the flow type transition occurs depends on the hydraulic system, fluid type, and flow conditions, as researchers have achieved values as high as Nonetheless, calculating the Reynolds number is a solid first step to figure out the approximate results to expect in reality for a given flow situation, and that is why engineers have been following that practice for more than a century now.

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It is mandatory to procure user consent prior to running these cookies on your website. Skip to content Home. Reynolds Number Calculator and Formula Equation.

September 22, EngineeringClicks. Characteristic distance or pipe diameterD: m in ft cm.Reynolds Number is a very important quantity for studying fluid flow patterns. It is a dimensionless parameter and widely used in fluid mechanics. Reynolds Number of a flowing fluid is defined as the ratio of inertia force to the viscous force of that fluid and it quantifies the relative importance of these two types of forces for given flow conditions.

reynolds number equation

The Reynolds number depends on the relative internal movement due to different fluid velocities. When viscous force dominates over the inertia force, the flow is smooth and at low velocities; the Reynolds Number value is comparatively less and flow is known as laminar flow.

On the other hand, when inertia force is dominant, the value of Reynolds number is comparatively higher and the fluid flows faster at higher velocities and the flow is called turbulent flow. With an increase in Reynolds Number the turbulence tendency of the flow increases.

However, note that the value of Reynolds number Re at which turbulent flow begins is dependent on the geometry of the fluid flow, which is different for pipe flow and external flow.

As the Reynolds Number is the ratio of two forces, there is no unit of Reynolds Number. So, in one sentence we can conclude that Reynolds Number is directly proportional to Flow Velocity, Characteristic Dimension, and Fluid Density while inversely proportional to fluid viscosity.

As Reynolds number is used for predicting laminar and turbulent flow, it is widely used as a design parameter for hydraulic and aerodynamic equipment. For the design of piping systems, aircraft wings, pumping system, scaling of fluid dynamic problems, etc Reynolds number serves as an important design tool. In the calculation of pressure drop and frictional losses, the Reynolds number plays an important role. The following diagram Fig. I am a Mechanical Engineer turned into a Piping Engineer.

I am very much passionate about blogging and always tried to do unique things. This website is my first venture into the world of blogging with the aim of connecting with other piping engineers around the world. I understood you explanation but could explain why the boundary layer thickness on a flat plate is proportional to the square root of the distance from the plate tip, and that the relative distance is inversely proportional to the Reynolds number?

Your email address will not be published. Save my name and email in this browser for the next time I comment. In recent times, FEA or Finite Element analysis is the most widely used method for solving engineering and mathematical models. Shear Modulus is defined as the ratio of shear stress to the corresponding shear strain within a material's proportional limit.

Also known as modulus of rigidity and rigidity modulus, the shear Skip to content Table of Contents. Leave a Reply Cancel reply Your email address will not be published. Continue Reading.