The Reynolds number is a dimensionless number used in fluid mechanics to determine the turbulence or absence of turbulence of a fluid. It is defined as the ratio of inertial forces to viscous forces and is named after Osborne Reynolds. The number is used in various applications, including friction factor calculations and modeling the flow of air around objects.
The Reynolds number (Re) is a dimensionless number related to fluid mechanics. It is among the most important attributes used to summarize the forces acting on a fluid and, based on its value, the turbulence or absence of turbulence of a fluid is determined. The designation is named after Osborne Reynolds, who did many pioneering studies of fluid mechanics in the late 19th and early 20th centuries. Changes in quantity are arranged on the X-axis of the Moody Chart, one of the most useful graphs in fluid mechanics.
More specifically, the Reynolds number is defined as the ratio of the inertial forces, which contribute to turbulence, to the viscous forces, which act against the turbulence, within a fluid. In other words, the number describes the probability of the flow being laminar or turbulent for a given set of physical conditions. Laminar or smooth flow means that everything in a fluid’s flow is moving in the same direction and these internal flows do not affect each other. Turbulent flow, on the other hand, indicates that breaks or eddies are created within the main flow.
The most common example of laminar and turbulent flow is found in a sink. When the water is first opened and it doesn’t run very fast, it is clear. Most internal water flows do not interact with each other and move in the same direction; this is laminar flow and indicates a low Reynolds number. As the amount and speed of the water increases, it turns white. Inland streams begin to collide with each other in a turbulent flow, introducing air into the water stream.
Another example of the concept is imagining an object moving through a fluid. The faster the object moves, the denser the liquid, and the longer the object moves, the more turbulent the fluid flow is likely to be. The more viscous or sticky a fluid is, the greater the chance that the thickness of the fluid will act against a turbulent flow.
Mathematically, the Reynolds number is defined as:
Re = ρ * V * L / µ
Where Re = Reynolds numberρ = fluid density (usually lb/ft3 or 3)V = velocity (usually ft/s or m/s)L = stroke length (usually ft om)
In a pipe or channel, L = hydraulic radius (usually ft or om)µ = fluid flow viscosity (usually lb/(ft*s) or kg/(m*s) or Pa*s)
From the equation it can be seen that the Reynolds number is directly proportional to the length. It also varies proportionally to the length and density of the fluid. The numbers ρ, V, and L all contribute to inertial forces, while µ contributes only to viscous forces.
For Re of 2.300 or less, fluid flow is considered laminar. Turbulent flow, on the other hand, occurs when Re is greater than 4.000. Values for the Reynolds number between these two quantities indicate transition flows, which can exhibit characteristics of either flow type.
The Reynolds number is used in many different applications of fluid mechanics. It is a necessary part of friction factor calculations in some fluid mechanics equations, such as the Darcy-Weisbach equation. Another common use of the number comes in the modeling of organisms that swim in water, and this application has been made from the largest animals, such as the blue whale, down to very small animals, including microorganisms. It also has applications in modeling the flow of air around objects, such as the wings of an aircraft.
Protect your devices with Threat Protection by NordVPN
