Reynold's Number

What is a Reynolds’s Number?

Reynolds’s number is a dimensionless quantity that is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe. Reynolds’s number is defined by the ratio of inertial forces to that of viscous forces.

It is given by the following relation:

\(Reynolds\;Number = \frac{Inertial\;Force}{Viscous\;Force}\)

Re = ρVD/μ


Re is the Reynolds’s number

ρ is the density of the fluid

V is the velocity of flow

D is the pipe diameter

μ is the viscosity of the fluid

If the Reynolds’s number calculated is high (greater than 2000), then the flow through the pipe is said to be turbulent. If Reynolds’s number is low (less than 2000), the flow is said to be laminar. Numerically, these are acceptable values, although in general the laminar and turbulent flows are classified according to a range. Laminar flow falls below Reynolds’s number of 1100 and turbulent falls in a range greater than 2200.

Laminar flow is the type of flow in which the fluid travels smoothly in regular paths. Conversely, turbulent flow isn’t smooth and follows an irregular maths with lots of mixing.

An illustration depicting laminar and turbulent flow is given below.

Reynolds Number

The Reynolds’s number is named after the British physicist Osborne Reynolds’s. He discovered this while observing different fluid flow characteristics like flow a liquid through a pipe and motion of an airplane wing through the air. He also observed that the type of flow can transition from laminar to turbulent quite suddenly.

Try the following application based problem to understand this concept.

Problem 1- Calculate Reynolds’s number, if a fluid having viscosity of 0.4 Ns/m2  and relative density of 900 Kg/m3  through a pipe of 20mm with a velocity of 2.5  2.5 m/

Solution 1 – Given that,

 Viscosity of fluid μ

\(\mu =\frac{0.4Ns}{m^{2}}\)

Density of fluid ρ


Diameter of the fluid

\(L=20\times 10^{-3}m\)

\(R_{e}=\frac{\rho VL}{\mu }\)

\(=\frac{900\times 2.5\times 20\times10^{-3}}{0.4}\)


From the above answer, we observe that the Reynolds number value is less than 2000. Therefore, the flow of liquid is laminar.

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Practise This Question

Water enters through end A with speed v1 and leaves through end B with speed v2 of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal and in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have v1 = v2 for