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where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.
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.
As can be seen, as the Damköhler number increases, the other term must decrease. The ensuing polynomial can be solved and the conversion for the rule of thumb Damköhler numbers found. Alternatively, one can graph the expressions and see where they intersect with the line given by the inverse Damköhler number to see the solution for conversion.
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
A typical absorption cross-section has units of cm 2 ⋅molecule −1. In honor of the fundamental contribution of Maria Goeppert Mayer to this area, the unit for the two-photon absorption cross section is named the "GM". One GM is 10 −50 cm 4 ⋅s⋅photon −1. [1] [2]
Gutmann, a chemist renowned for his work on non-aqueous solvents, described an acceptor-number scale for solvent Lewis acidity [4] with two reference points relating to the 31 P NMR chemical shift of Et 3 PO in the weakly Lewis acidic solvent hexane (δ = 41.0 ppm, AN 0) and in the strongly Lewis acidic solvent SbCl 5 (δ = 86.1 ppm, AN 100).
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate ( convection + diffusion) to the rate of diffusive mass transport, [ 1 ] and is named in honor of Thomas Kilgore Sherwood .
The Deborah number is the ratio of fundamentally different characteristic times. The Deborah number is defined as the ratio of the time it takes for a material to adjust to applied stresses or deformations, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material: