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The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.
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 original paper by Gurney analyzed the situation of an exploding shell or bomb, a mass of explosives surrounded by a solid shell. Other researchers have extended similar methods of analysis to other geometries. All of the equations derived based on Gurney's methods are collectively called "Gurney equations".
D 50: Mass-median-diameter (MMD). The log-normal distribution mass median diameter. The MMD is considered to be the average particle diameter by mass. σ g: Geometric standard deviation. This value is determined mathematically by the equation: σ g = D 84.13 /D 50 = D 50 /D 15.87. The value of σ g determines the slope of the least-squares ...
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The kinetic diameter is not the same as atomic diameter defined in terms of the size of the atom's electron shell, which is generally a lot smaller, depending on the exact definition used. Rather, it is the size of the sphere of influence that can lead to a scattering event. [1] Kinetic diameter is related to the mean free path of molecules in ...
For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere, such that the motion of the sphere does not disturb that reference parcel of fluid. The density and viscosity are those belonging to the fluid. [23]
The number density is defined as the number of molecules per (extensive) volume = /. The collision cross section per volume or collision cross section density is C σ {\displaystyle C\sigma } , and it is related to the mean free path l {\displaystyle l} by