Search results
Results From The WOW.Com Content Network
The equation is named after Lord Rayleigh, who introduced it in 1880. [2] The Orr–Sommerfeld equation – introduced later, for the study of stability of parallel viscous flow – reduces to Rayleigh's equation when the viscosity is zero. [3] Rayleigh's equation, together with appropriate boundary conditions, most often poses an eigenvalue ...
The above equation can be used to plot the Rayleigh line on a Mach number versus ΔS graph, but the dimensionless enthalpy, H, versus ΔS diagram, is more often used. The dimensionless enthalpy equation is shown below with an equation relating the static temperature with its value at the choke location for a calorically perfect gas where the ...
The critical Rayleigh number can be obtained analytically for a number of different boundary conditions by doing a perturbation analysis on the linearized equations in the stable state. [16] The simplest case is that of two free boundaries, which Lord Rayleigh solved in 1916, obtaining Ra = 27 ⁄ 4 π 4 ≈ 657.51. [17]
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [ 2 ] [ 3 ] [ 4 ] It characterises the fluid's flow regime: [ 5 ] a value in a certain lower range denotes laminar flow ; a value in a higher range ...
Rayleigh-type λ −4 scattering can also be exhibited by porous materials. An example is the strong optical scattering by nanoporous materials. [ 23 ] The strong contrast in refractive index between pores and solid parts of sintered alumina results in very strong scattering, with light completely changing direction each five micrometers on ...
The Rayleigh–Plesset equation is often applied to the study of cavitation bubbles, shown here forming behind a propeller.. In fluid mechanics, the Rayleigh–Plesset equation or Besant–Rayleigh–Plesset equation is a nonlinear ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of incompressible fluid.
The equations can be used to describe an isotope fractionation process if: (1) material is continuously removed from a mixed system containing molecules of two or more isotopic species (e.g., water with 18 O and 16 O, or sulfate with 34 S and 32 S), (2) the fractionation accompanying the removal process at any instance is described by the ...
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .