Rayleigh’s equation

The result is Rayleigh s equation for the probability density of the velocity of a heavy particle,... 

Utilizing the scatter term of Rayleigh s equation as simplified above we have... 

Light scattered by small particles will be completely polarized if they are optically isotropic and distributed entirely at random. This polarization will take place in any plane normal to the scattered rays. In practice complete polarization by a suspension of particles is never realized, and consequently suitable corrections must be applied to Rayleigh s equation to account for the shape of the particles. 

Poisson gave the first three terms of Rayleigh s equation (9), in 1831, and Laplace, the first two terms on the right-hand side of equation (10) for wide tubes, in 1805. Bosanquet1 has calculated the corrections for moderately wide tubes, using a different method of approximation from that of Bashforth and Adams. Porter8 has given further calculations of the corrections. 

Even in the first publications concerning the copolymerization theory [11, 12] their authors noticed a certain similarity between the processes of copolymerization and distillation of binary liquid mixtures since both of them are described by the same Lord Rayleigh s equations. The origin of the term azeotropic copolymerization comes just from this similarity, when the copolymer composition coincides with monomer feed composition and does not drift with conversion. Many years later the formal similarity in the mathematical description of copolymerization and distillation processes was used again in [13], the authors of which, for the first time, classified the processes of terpolymerization from the viewpoint of their dynamics. The principles on which such a classification for any monomer number m is based are presented in Sect. 5, where there is also demonstrated how these principles can be used for the copolymerization when m = 3 and m = 4. 

For each x between x(0) and x(t), we can look up the corresponding y(t) and compute the integrand in Rayleigh s equation l/(y-x). The integral is the area under the curve between these two limits. 

The last section in this chapter is a brief introduction to stability of parallel shear flows. We consider three basic issues (i) Rayleigh s equation for inviscid flows, (ii) Rayleigh s necessary condition on an inflection point for inviscid instability, and (iii) a derivation of the Orr-Sommerfeld equation and Squire s theorem. 

The above-mentioned resist classification based on radiation sources/expo-sure wavelength is the reflection of the industry s quest for higher resolution. The lithographic resolution (R) is proportional to the exposing wavelength (A) and inversely proportional to the numerical aperture (NA) of the lens (Rayleigh s equation) ... 

Rayleigh s Equations Definition of Reduced Intensity and Turbidity. 

Eq. (6.182) is known as Rayleigh s equation. This equation describes the time rate of change of the bubble s radius due to the change of pressure difference inside and outside the bubble. 

The dynamic balance equation for the bubble, known as Rayleigh s equation, looks like... 

It is reported by Whelehan and Marison and by Brandenberger et al. that Rayleigh s equation was extended further by Weber who included the effect of viscosity q into the... 

Batch Dehydration of Benzene. As another example of the use of Rayleigh s equation, consider the dehydration of benzene. Benzene saturated with water at 20 0. contains 0.25 mol per cent water, and it is to be given a simple differential distillation at a constant pressure of 1 atm. The operation is to proceed until the mol per cent water in the liquid remaining in the still is 0.00025. The following data and simplifying assumptions will be used in the calculations ... 

Illustration 7.4 Rayleigh s Equation in the Environment Attenuation of Mercury Pollution in a Water Basin... 

We consider here a body of water containing dissolved mercury at the saturation level and set ourselves the task of calculating the reduction in mercury content that occurs when 0.01% of the contents is evaporated. It is assumed that the vapor in question is at all times in equilibrium with a well-mixed liquid, i.e., that Rayleigh s equation applies. 

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