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Fluid dynamicists define the chord Reynolds number R = Vc/ν, where V is the flight speed, c is the chord length, and ν is the kinematic viscosity of the fluid in which the airfoil operates, which is 1.460 × 10 −5 m 2 /s for the atmosphere at sea level. [19]
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. [2]
The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
μ = Dynamic viscosity (SI units: N s/m 2) ʋ = Kinematic viscosity (SI units: m 2 /s) There are few ways to maintain kinematic similarity. To keep the Reynolds number the same, the scaled-up model can use a different fluid with different viscosity or density. We can also change the velocity of the fluid to maintain the same dynamic ...
= is the kinematic viscosity – it measures the ratio of dynamic viscosity to the density of the fluid The Reynolds number is useful because it can provide cut off points for when flow is stable or unstable, namely the Critical Reynolds number R c {\displaystyle R_{c}} .
μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/(m·s)); ν is the kinematic viscosity of the fluid, ν = μ / ρ (m 2 /s); ρ is the density of the fluid (kg/m 3). For such systems, laminar flow occurs when the Reynolds number is below a critical value of approximately 2,040, though the transition range is typically ...