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In fluid dynamics, the Reynolds number ... In some special studies a characteristic length other than chord may be used; rare is the "span Reynolds number", which is ...
A characteristic length is usually the volume of a system divided by its surface: [2] = For example, it is used to calculate flow through circular and non-circular tubes in order to examine flow conditions (i.e., the Reynolds number).
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.
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 ...
is the Reynolds number with the cylinder diameter as its characteristic length; is the Prandtl number. The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above.
is the characteristic length of the system ν = μ ρ {\displaystyle \nu ={\frac {\mu }{\rho }}} 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 ...
where L is the characteristic length, u the local flow velocity, D the mass diffusion coefficient, Re the Reynolds number, Sc the Schmidt number, Pr the Prandtl number, and α the thermal diffusivity, = where k is the thermal conductivity, ρ the density, and c p the specific heat capacity.
The dimensionless magnetic Reynolds number, , is also used in cases where there is no physical fluid involved. = × (characteristic length) × (characteristic velocity) where is the magnetic permeability is the electrical conductivity.