This concept was introduced by George Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds who popularized its use in 1883.
The Reynolds Number is a dimensionless quantity that helps to predict the fluid flow patterns in different situations such as liquid flow in a pipe or air over an aircraft wing. It is the ratio of inertial forces to viscous forces within a fluid.
It's used to determine whether a fluid flow is laminar (smooth and orderly), turbulent (chaotic and irregular) or transitional.
When water first comes out of a tap, it often has a smooth, clear appearance. This is laminar flow. As the water falls further, it starts to become more disturbed and splash, this is turbulent flow.
In smaller blood vessels, the flow is laminar, while in larger arteries, it may become transitional or even turbulent.
Reynolds Number can be calculated by using the following formula:
$$R_e = \frac {𝜌.𝑣.L} {𝜇}$$
Where:
𝜌 = Fluid density
𝑣 = Flow velocity
𝐿 = Length or diameter of a pipe
𝜇 = Dynamic viscosity of the fluid
- If the Reynolds number is below 2000, the flow is laminar, that means the water flows smoothly in layers.
- If the Reynolds number is above 4000, the flow is turbulent, that means the water flow is chaotic with eddies and mixing.
- If the flow between those numbers is considered transitional.
Determine the flow of fluid having a relative density of 100 kg/m3, the viscosity of 0.5 Ns/m2 with a velocity of 5 m/s through a pipe of 0.2 m.
Given:
Velocity of fluid (𝑣) = 5 m/s
Diameter of pipe (𝐿) = 0.2 m
Relative density of fluid (𝜌) = 100 kg/m3
Viscosity of fluid (𝜇) = 0.5 Ns/m2
Putting these values in the equation $R_e = \frac {𝜌.𝑣.L} {𝜇}$
we get-
Re = (100 kg/m3)(5 m/s)(0.2 m)/(0.5 Ns/m2)
or, Re = 200
Since, the Reynolds number is less than 2000, the flow of liquid is laminar.