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In those cases, the characteristic length is the diameter of the pipe or, in case of non-circular tubes, its hydraulic diameter : = Where is the cross-sectional area of the pipe and is its wetted perimeter. It is defined such that it reduces to a circular diameter of D for circular pipes.
Some texts then use a characteristic dimension that is four times the hydraulic radius, chosen because it gives the same value of Re for the onset of turbulence as in pipe flow, [17] while others use the hydraulic radius as the characteristic length-scale with consequently different values of Re for transition and turbulent flow.
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.
x is the characteristic length; Ra x is the Rayleigh number for characteristic length x; g is acceleration due to gravity; β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature
[1]: 336 A value between one and 10 is characteristic of slug flow or laminar flow. [2] A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. [2] A similar non-dimensional property is the Biot number, which concerns thermal conductivity for a solid body rather than a fluid.
The characteristic length depends on the geometry. For a circular pipe the characteristic length would be the diameter. For non circular ducts, the characteristic length would be: L=4A/p where A is the cross-sectional area of the duct, P would be the wetted perimeter. Note that for a circular pipe: L=4*(pi*D^2/4)/(pi*D) = D
This number should not be confused with the Darcy friction factor which applies to pressure drop in a pipe. It is defined as = where K is the permeability of the medium (SI units: m 2); d is the characteristic length, e.g. the diameter of the particle (SI units: m). [1]
L is a characteristic length (m) D is mass diffusivity (m 2 s −1) h is the convective mass transfer film coefficient (m s −1) Using dimensional analysis, it can also be further defined as a function of the Reynolds and Schmidt numbers: = (,)