In fluid mechanics, Reynolds number (Re) is the ratio of a fluid’s inertial forces (vs d) to viscosity forces (μ/ρ), and as a result, this value gives the relative importance of these two types of forces to each other under a certain flow condition. Therefore, the Reynolds number is used to characterize different flow regimes such as laminar flow and turbulent flow.
It is one of the most important of the other coefficients used together in fluid mechanics and is used to define dynamic similarity. Two geometrically similar flow patterns are said to be dynamically similar if they have the same relative coefficient, even if they are in two different liquids with different flow values.
Reynolds Number
Reynolds number is named after Osborne Reynolds, who lived between 1842 and 1912 and defined this number.
Reynolds Number is the ratio of the inertial force of a fluid to its viscous force. Also, inertia force is the momentum force of the mass of a flowing stream. It is a measure of how difficult it would be to fundamentally adjust the speed of a moving stream. Viscous force is the force that deals with the friction of a flowing liquid. Also, inertial and viscous forces are quite similar. They also share the same unit, meaning the Reynolds number is unit less.
Reynolds Number Formula
It is typically defined as follows:
vs – speed of the fluid
d – pipe diameter
μ – dynamic viscosity of the fluid
ν – kinematic viscosity of the fluid: ν = μ / ρ
ρ – density of the fluid
When the Reynolds number is calculated, if the resulting number is high, the flow in the pipe is considered turbulent. If the Reynolds number is low, the flow is considered laminar. All values are acceptable numerical data; Laminar and turbulent flows are generally grouped within a range. While the Reynolds number of laminar flow is less than 2000, the Reynolds number of turbulent flow is greater than 2000.
The generally accepted value of the critical Reynolds number for internal flow in a circular pipe is 2300.
Reynolds Number Usage Areas
1) Reynolds number plays an important role in calculating the friction factor in several equations in fluid mechanics, including the Darcy-Weisbach equation.
2) It is used when modeling the movements of organisms swimming in water.
3) Atmospheric air is considered a fluid. Hence, Reynolds number can be calculated for this. This makes it possible to apply it in wind tunnel testing to study the aerodynamic properties of various surfaces.
4) It plays an important role in testing wind lift in aircraft, especially in supersonic flights where high speed causes a local increase in the density of the air surrounding aircraft.
