"In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces."
Dimensionless quantity used to predict fluid flow patterns and behavior.
Fluid Properties: Basic properties of fluids such as density, viscosity, velocity, pressure, and different types of fluids.
Dimensional Analysis: The study of relationships between different physical quantities that are expressed in terms of their dimensions.
Navier-Stokes Equations: A set of equations governing the motion of viscous fluids.
Turbulence: The irregular and chaotic motion of fluids resulting in turbulent flow.
Boundary Layers: The thin layer of fluid that forms near the surface of a solid object in contact with fluid.
Reynold's Experiment: The experiment conducted by Osborne Reynolds which led to the discovery of Reynold's number, its significance, and its range of values.
Flow Regimes: The different types of flow regimes such as laminar, transitional, and turbulent flow.
Imposing Boundary Conditions: Understanding and imposing boundary conditions such as no-slip boundary, free-slip boundary, and prescribed velocity or pressure boundary conditions.
Hydraulic Resistance: The opposition of the fluid flow in a circuit that is proportional to the velocity of the fluid through it.
Applications of Reynold's Number: The applications of Reynold's number in the analysis and prediction of fluid flow behavior in various engineering applications such as pipes, ships, airplane wings, heat exchangers, and more.
Hydraulic Reynolds number: This is also known as the Darcy-Weisbach equation and is given by Re = 4Q/πDv, where Q is the volumetric flow rate, D is the diameter of the pipe, and v is the kinematic viscosity of the fluid. This Reynolds number is used in pipe flow problems and is used to predict the onset of turbulence.
Hydrodynamic Reynolds number: This is given by Re = U*L/ν, where U is the characteristic velocity of the fluid, L is the characteristic length scale of the system, and ν is the kinematic viscosity. It is used to describe the flow around solid objects such as ships and airplanes.
Mach Reynolds number: This is given by Re = U/a, where U is the characteristic velocity of the fluid and a is the speed of sound in the fluid. It is used to describe the flow of compressible fluids such as gases around objects.
Thermal Reynolds number: This is given by Re = ρUL/κ, where ρ is the density of the fluid, U is the characteristic velocity of the fluid, L is the characteristic length scale of the system, and κ is the thermal diffusivity of the fluid. It is used to describe the flow of fluids in which thermal effects are important.
Magnetic Reynolds number: This is given by Re_m = UL/η, where η is the magnetic diffusivity of the fluid. It is used to describe the flow of electrically conducting fluids in the presence of a magnetic field.
Low Reynolds number: This refers to flows with very small Reynolds numbers, typically less than 1. In such flows, viscous forces dominate over inertial forces, leading to laminar flow. This is often seen in microfluidic devices and small-scale fluid systems.
High Reynolds number: This refers to flows with very large Reynolds numbers, typically greater than 10^4. In such flows, inertial forces dominate over viscous forces, leading to turbulent flow. This is seen in many industrial and natural fluid systems.
"At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow."
"At high Reynolds numbers, flows tend to be turbulent."
"The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents)."
"These eddy currents begin to churn the flow, using up energy in the process."
"For liquids, turbulence increases the chances of cavitation."
"The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing."
"It is used to predict the transition from laminar to turbulent flow."
"The Reynolds number is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version."
"The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behavior on a larger scale."
"Fluid behavior on a larger scale, such as in local or global air or water movement, and thereby the associated meteorological and climatological effects."
"The concept was introduced by George Stokes in 1851."
"The Reynolds number was named by Arnold Sommerfeld in 1908."
"Osborne Reynolds (1842–1912) popularized its use in 1883."
"The concept was introduced by George Stokes in 1851."
"The Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations."
"The Reynolds number measures the ratio between inertial and viscous forces."
"At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow."
"The turbulence results from differences in the fluid's speed and direction."
"These eddy currents begin to churn the flow, using up energy in the process."