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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
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 value for ...
The Fanning friction factor (named after American engineer John T. Fanning) is a dimensionless number used as a local parameter in continuum mechanics calculations. It is defined as the ratio between the local shear stress and the local flow kinetic energy density: [1] [2]
In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point.These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states.
If the speed of sound is not known, Mach number may be determined by measuring the various air pressures (static and dynamic) and using the following formula that is derived from Bernoulli's equation for Mach numbers less than 1.0. Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is: [8]
These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. [1]
Conversion and its related terms yield and selectivity are important terms in chemical reaction engineering.They are described as ratios of how much of a reactant has reacted (X — conversion, normally between zero and one), how much of a desired product was formed (Y — yield, normally also between zero and one) and how much desired product was formed in ratio to the undesired product(s) (S ...
Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. From FLRW metric we compute Christoffel symbols, then the Ricci tensor. With the stress–energy tensor for a perfect fluid, we substitute them into Einstein's field equations and the resulting equations are described below.