## Reynolds Number

**Introduction to Reynolds number:**

The Reynolds number was given by the British scientist Osborne Reynolds in 1883. He is famous for his work in hydraulics and hydrodynamics. He was born into a family of Anglican clerics and he graduated at Queens’s College, Cambridge, in mathematics in 1867 and became the first professor of engineering at Owens College, Manchester, in year 1868 and retired from the same college in 1905. In 1877, he was a fellow of the Royal Society in 1877 and received a Royal Medal in 1888. Understanding The Shorter the Wavelength of Visible Light the is always challenging for me but thanks to all math help websites to help me out.

**Reynolds Number:**

Osborne Reynolds discovered the ratio that has since been called the Reynolds number when observing fluid flow characteristics that means how a liquid flows in a pipe or how air flows across an aircraft wing. Reynolds explained that the motion of a fluid may be either laminar (in smooth layers) or turbulent, and that the change from a laminar flow to a turbulent flow can happen suddenly. Reynolds proved experimentally that in case of a viscous fluid, the critical velocity is given by:

vc = Nη / ρ D

Where, D = diameter of the tube through the liquid flows, N = Reynolds Number, = density of the fluid, η = coefficient of viscosity

Reynolds Number = N = ρD vc /η

**Use of Reynolds Number:**

Reynolds Number is a dimensionless constant. Reynolds number determines the flow of liquid. If the value of Reynolds number is less than about 2,000, flow in a pipe is generally laminar, whereas, at values greater than 2,000, flow is usually turbulent. The flow of the fluid becomes laminar to turbulent at not any specific value of the Reynolds number but in a range usually beginning between 1,000 to 2,000.

**Example to Calculate the Reynolds Number:**

A fluid of viscosity of 0.4 Ns/m2 and relative density of 0.9 flows through a 20 mm diameter pipe with a velocity of 2.5 m/s. Find the Reynolds number.

Solution

The density can be calculated using the relative density as

ρ = 0.9 x 1000 kg/m3 = 900 kg/m3

The Reynolds Number can then be calculated by using the formula given below

=Reynolds Number = N = ρD vc /η = 900 x 20 x 10 -3 x 2.5 / 0.4

N = 112.5

Here we observe that the value of Reynolds number is less than 2000, so the flow of liquid is laminar.