Reynolds Number is 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 important 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 Numbers in the year 1883.
The Formula for Reynolds Number
The formula for Reynolds Number is as given below
[ Re = frac{(ρuL)}{μ} = frac{(uL)}{ν}]
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
Reynolds Number-Its Application in Fluid Mechanics
The Reynolds number is used to study fluids as they flow. The Reynolds number determines whether a fluid flow is steady or unsteady. (laminar and turbulent) If a flow is laminar, fluids will move along smooth streamlines. If the flow is turbulent, these streamlines break up and the fluid will move irregularly.
It is used when modelling the movement of organisms swimming through water. 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.
Reynolds number, in fluid mechanics, is a criterion of whether the fluid (liquid or gas) flow is steady (streamlined, or laminar) or on average steady with small unsteady fluctuations (turbulent).
The transition between fluids from laminar to turbulent occurs very suddenly.
Reynolds number is given by
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Reynolds Number = Inertial Force / Viscous Force |
It is used when modeling the movement of organisms swimming through water. It is based on various factors like velocity, pressure, heat and temperature.
The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number (Re) of a flowing fluid is computed by multiplying the fluid velocity by the pipe’s internal diameter (to obtain the inertia force of the fluid) and then by dividing the result by the kinematic viscosity (viscous force per unit of length).
Number Range
Actually, the transition between laminar and turbulent flow occurs not at a specific value of the Reynolds number but in a range usually beginning between 1,000 to 2,000 and extending upward to between 3,000 and 5,000.
The maximum range is between 2300 to 4000.The Turbulent flow occurs over a range of Reynolds numbers from approximately 2,300 to 4,000, regardless of the nature of the fluid or the dimensions of the pipe or the average velocity. All that matters is that this specific combination of the parameters, known as the Reynolds number, fall in the range indicated.
Types of Fluid Flow in Fluid Mechanics
The different types of fluid flow are:
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Steady and Unsteady Flow.
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Uniform and Non-Uniform Flow.
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Laminar and Turbulent Flow.
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Compressible and Incompressible Flow.
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Rotational and Irrotational Flow.
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One, Two and Three -dimensional Flow