Reynolds Number

Reynolds number is a dimensionless quantity. It is the ratio between the inertial and viscous forces of the fluid.

Where

ρ is the density of the fluid

V is the velocity of the flow

L is the characterizing length in the flow system (usually the diameter of the pipe)

μ is the viscosity of the fluid

The number helps to categorize laminar flow from turbulent flow of any fluid like air or water. Laminar flow refers to the smooth and steady flow. It is also known as streamline flow. On the other hand, turbulent flow is irregular and chaotic due to the fluid’s changing velocity. If Re < 2000, the flow is laminar. If Re > 2000, the flow is turbulent.

Unit and Dimension

Reynolds number is a dimensionless quantity and does not have any unit. We can prove it by taking the division of inertial force and viscous force dimensions.

The critical Reynolds number determines the transition from laminar to turbulent flow for a particular fluid system as the flow rate increases. It is a limit where the laminar flow changes to turbulent flow. If the calculated Reynolds number is greater than the critical Reynolds number, the flow regime is turbulent; otherwise, the flow regime is laminar. For a Newtonian fluid, a value of 2100 is taken as the critical Reynolds number.

Problem 1: Determine the fluid flow with a relative density of 80 kg/m³, a viscosity of 0.7 Nˑs/m², and a velocity of 6 m/s through a pipe of 0.25 m diameter.

Solution

Given

ρ = 80 kgˑm^-3      V = 6 mˑs^-1           L = 0.25 m            μ = 0.7 Nˑsˑm^-2 = 0.7 kgˑmˑs^-2ˑsˑm^-2 = 0.7 kgˑm^-1ˑs^-1

The Reynolds Number is

Re = ρVL/μ

=> Re = (80 kgˑm^-3 x 6 mˑs^-1 x 0.25 m)/0.7 kgˑm^-1ˑs^-1

=> Re = 120 kgˑm^-1ˑs^-1ˑ/0.7 kgˑm^-1ˑs^-1

=> Re = 171

Since Re < 2000, the flow is Laminar.