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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]
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.
The equation can either be used with consistent units or nondimensionalized. The Reynolds Equation assumes: The fluid is Newtonian. Fluid viscous forces dominate over fluid inertia forces. This is the principle of the Reynolds number. Fluid body forces are negligible.
From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...
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 ...
The local mean magnetic field scales as /, substitution of which in Dobrowolny's equation yields Kolmogorov's energy spectrum for MHD turbulence. Renormalization group analysis have been also performed for computing the renormalized viscosity and resistivity.
where is the gap width between the plates, is the characteristic velocity scale, is the characteristic length scale in directions parallel to the plate and is the kinematic viscosity. Specifically, the Reynolds number R e = U h / ν {\displaystyle Re=Uh/\nu } need not always be small, but can be order unity or greater as long as it satisfies ...
In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum.