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spherical shell, right: two halves. In geometry, a spherical shell (a ball shell) is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii. [1]
If a given particle is taken to be at the origin O, and if = / is the average number density of particles, then the local time-averaged density at a distance from O is (). This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.
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.
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 ...
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.
A proof of the recursion formula relating the volume of the n-ball and an (n − 2)-ball can be given using the proportionality formula above and integration in cylindrical coordinates. Fix a plane through the center of the ball. Let r denote the distance between a point in the plane and the center of the sphere, and let θ denote the azimuth.
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 ...
In Schrödinger's quantum-mechanical theory of the hydrogen atom, the Bohr radius is the value of the radial coordinate for which the radial probability density of the electron position is highest. The expected value of the radial distance of the electron, by contrast, is 3 2 a 0 {\displaystyle {\tfrac {3}{2}}a_{0}} .