Fluid Mechanics – Reynolds Number

In fluid mechanics, Reynolds Number (Re) is most important dimensionless number. Reynolds Number is used to determine whether fluid flow is laminar or turbulent. It is one of main controlling parameters in all viscous flow where numerical model is selected according to pre-calculated Reynolds Number. This article gives you detailed introduction into topic of Reynolds Number and its application.

What is Reynolds Number?

Reynolds Number is ratio of internal force to viscous force. This Reynolds Number was named by Arnold Sommerfeld. Also, it is dimensionless important parameter in fluid mechanics that helps to forecast flow outline in different fluid flow situations. Read more about Fluid Mechanics – Gas Laws

Re can be used to find out change from laminar to turbulent flow. Since inertial forces cause turbulent flow, that means as Reynolds Number increased then fluid show more turbulence. Whereas smaller Reynolds Number is take place laminar flow of fluid.

Reynolds Number Formula

In fluid mechanics, Reynolds Number is dimensionless value to be whether the fluid flow is steady or turbulent to many properties. Such as velocity, length, viscosity and also type of flow. Therefore it is expressed as ratio of inertial forces to viscous forces and cab is explained in terms of units and parameters. This value gets by comparing inertial force with viscous force. An increasing Reynolds Number shows an increasing turbulence of flow.

Reynolds Number id denoted by Re.

Re=\frac{inertial\quad force}{viscous\quad force}=\frac{fluid\quad and \quad flow\quad properties}{fluid\quad properties}

Reynolds Number is defined as


Reynolds number formula can be used in the problems to calculate the Velocity (V), density (ρ), Viscosity (μ) and diameter (L) of the liquid.

  • D is the characteristic length [m]
  • v is the average velocity of the flow [m/s],
  • p is the weight density [kg/m3] and
  • µ is the dynamic (or absolute) viscosity of the fluid [Pa s].

Reynolds Number is defined for several different situations where fluid is in relative motion to surface. These include fluid properties of density and viscosity, plus velocity and characteristic length or dimension. Reynolds Number differs depending on specifications of fluid flow such as variation of density, variation of viscosity being internal or external flow etc.

Reynolds Number of fluid flow

As Reynolds Number is ratio, so it has no units. There are two types of fluid flow like Laminar Flow and Turbulent Flow. Check Viscosity in Fluid Mechanics

Laminar Flow

Laminar flow is type of flow in which fluid particles move in smooth layers is called laminar flow. And this layers which never interfere with one another. As result of laminar flow is that velocity of fluid is constant at any point in fluid. In laminar flow, fluid particles move in layer sliding smoothly over next layer and streamlines are straight and parallel. It is also called viscous flow or streamlines flow.

For example: – Flow through pipe of uniform cross-section.

Turbulent flow

Turbulent flow is defined as flow in which fluid particles move is zigzag way. This type of flow in which fluid particles does not move in layers is called turbulent flow. These fluid particles cross paths of each other and velocity of this fluid is not constant at every point. For examples of both laminar and turbulent flows can be seen in cigarette smoke.

For example

  • Flow in river at time of flood
  • Flow through pipe of different cross-section

Types of fluid flows based on Reynolds Number

Reynolds Number can be used to determine if flow is laminar, transient or turbulent. Following are flow of fluid is-

  • If Re < 2000, the flow is called Laminar
  • If Re > 4000, the flow is called turbulent
  • If 2000 < Re < 4000, the flow is called transition.

Significance of Reynolds Number

Reynolds Number is important that we can estimate whether flow is laminar or turbulent. Laminar flow occurs at low Reynolds Number. We can see Reynolds Number will be low if viscous forces are dominant. And flow will turbulent at high Reynolds Number when internal forces will be high.

Applications of Reynolds Number

  • Reynolds Number plays important parts in friction calculation incase of frictional loss in pipes know as Darch – Weisbach equation.
  • Thus this number is measure type of behavior of flowing fluid and can be used in real life applications, such as for designing fountain heads, water tubes and pumps etc.
  • Hence, Air is fluid and it can be applied on wind tunnel testing to study aerodynamic properties of various surfaces.