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μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/m·s) ρ is the density of the fluid (kg/m 3) Pe is the Peclet Number; Re is the Reynolds Number. The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is the Lewis number (Le).
The principle of corresponding states (CS principle or CSP) was first formulated by van der Waals, and it says that two fluids (subscript a and z) of a group (e.g. fluids of non-polar molecules) have approximately the same reduced molar volume (or reduced compressibility factor) when compared at the same reduced temperature and reduced pressure ...
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 ratio of the Grashof number to the square of the Reynolds number may be used to determine if forced or free convection may be neglected for a system, or if there's a combination of the two. This characteristic ratio is known as the Richardson number (Ri). If the ratio is much less than one, then free convection may be ignored.
Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. [1] For liquids, it corresponds to the informal concept of thickness; for example, syrup has a higher viscosity than water. [2]
Physically, volume viscosity represents the irreversible resistance, over and above the reversible resistance caused by isentropic bulk modulus, to a compression or expansion of a fluid. [1] At the molecular level, it stems from the finite time required for energy injected in the system to be distributed among the rotational and vibrational ...
Name Standard symbol Definition Field of application Archimedes number: Ar = fluid mechanics (motion of fluids due to density differences) : Asakuma number: As = heat transfer (ratio of heat generation of microwave dielectric heating to thermal diffusion [6]
The following table lists historical approximations to the Colebrook–White relation [23] for pressure-driven flow. Churchill equation [ 24 ] (1977) is the only equation that can be evaluated for very slow flow (Reynolds number < 1), but the Cheng (2008), [ 25 ] and Bellos et al. (2018) [ 8 ] equations also return an approximately correct ...
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