Introduction: In fluid mechanics, the Reynolds number is a dimensionless quantity that describes the ratio of inertial forces to viscous forces in a fluid flow. It is named after Osborne Reynolds, who first described this concept in 1883.
The Reynolds number is used to predict the flow characteristics of fluids in a wide range of applications. In this article, we will explain what the Reynolds number is, and its formula, and provide some examples of how it can be used in practical situations.
What is the Reynolds number?
The Reynolds number is a dimensionless quantity that relates the inertial forces to the viscous forces in a fluid flow. It is given by the following formula:
Re = ρvd/μ
where:
Re is the Reynolds number
ρ is the density of the fluid
v is the velocity of the fluid
d is a characteristic length of the flow, such as the diameter of a pipe
μ is the dynamic viscosity of the fluid
The Reynolds number is a measure of the tendency of a fluid to undergo turbulent flow. When the Reynolds number is low, the flow is laminar, in this fluid moves in smooth layers that do not mix. When the Reynolds number is high, the flow becomes turbulent, which means that the fluid moves in a chaotic manner, with eddies and vortices forming.
Please refer to the below image for a better understanding:
The Reynolds number is a dimensionless quantity, which does not depend on the units used to measure the different parameters in the formula. This makes it a useful tool for comparing flows in different situations, as long as the fluids involved have similar properties.
To better understand the Reynolds number and its use, let’s look at some examples of its application.
Example 1: Flow in a pipe
Consider the flow of water through a pipe with a diameter of 10 cm at a velocity of 1 m/s. The density of water at room temperature is approximately 1000 kg/m3, and its dynamic viscosity is approximately 0.001 Pa·s. Using the formula for the Reynolds number, we can calculate:
Re = ρvd/μ = (1000 kg/m3) × (1 m/s) × (0.1 m) / (0.001 Pa·s) ≈ 100000
This value of the Reynolds number indicates that the water flow through the pipe is likely to be turbulent. This means that the water is likely to experience a significant amount of mixing and disruption as it flows through the pipe, which can have implications for the efficiency of the flow and the energy required to pump the water.