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The collision cross section per volume or collision cross section density is , and it is related to the mean free path by l = 1 2 C σ {\displaystyle l={\frac {1}{{\sqrt {2}}C\sigma }}} Combining the kinetic equations for molecular motion with the defining equation of shear viscosity gives the well known equation for shear viscosity for dilute ...
On average, transfers energy from large to small scales. However, instantaneously Π {\displaystyle \Pi } can be positive or negative, meaning it can also act as a source term for E f {\displaystyle E_{f}} , the kinetic energy of the filtered velocity field.
Favre averaging is the density-weighted averaging method, used in variable density or compressible turbulent flows, in place of the Reynolds averaging.The method was introduced formally by the French physicist Alexandre Favre in 1965, [1] [2] although Osborne Reynolds had also already introduced the density-weighted averaging in 1895. [3]
The TKE can be defined to be half the sum of the variances σ² (square of standard deviations σ) of the fluctuating velocity components: = (+ +) = ((′) ¯ + (′) ¯ + (′) ¯), where each turbulent velocity component is the difference between the instantaneous and the average velocity: ′ = ¯ (Reynolds decomposition).
In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus.
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
In physics, and especially scattering theory, the momentum-transfer cross section (sometimes known as the momentum-transport cross section [1]) is an effective scattering cross section useful for describing the average momentum transferred from a particle when it collides with a target. Essentially, it contains all the information about a ...
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.