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Williams Spray Equation
In combustion, the Williams spray equation, also known as the Williams–Boltzmann equation, describes the statistical evolution of sprays contained in another fluid, analogous to the Boltzmann equation for the molecules, named after Forman A. Williams, who derived the equation in 1958. Mathematical description The sprays are assumed to be spherical with radius r, even though the assumption is valid for solid particles(liquid droplets) when their shape has no consequence on the combustion. For liquid droplets to be nearly spherical, the spray has to be dilute(total volume occupied by the sprays is much less than the volume of the gas) and the Weber number We = 2r\rho_g, \mathbf-\mathbf, ^2/\sigma, where \rho_g is the gas density, \mathbf is the spray droplet velocity, \mathbf is the gas velocity and \sigma is the surface tension of the liquid spray, should be We \ll 10. The equation is described by a number density function f_j(r,\mathbf,\mathbf,T,t) \, dr \, d\mathbf \, d\mathbf\,d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While the activation energy must be overcome to initiate combustion (e.g., using a lit match to light a fire), the heat from a flame may provide enough energy to make the reaction self-sustaining. Combustion is often a complicated sequence of elementary radical reactions. Solid fuels, such as wood and coal, first undergo endothermic pyrolysis to produce gaseous fuels whose combustion then supplies the heat required to produce more of them. Combustion is often hot enough that incandescent light in the form of either glowing or a flame is produced. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Equation
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerner, G. L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that describes the change of a macroscopic quantity in a thermodynamic system, such as energy, charge or particle number. The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the positio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forman A
Forman may refer to: Places: *Forman, North Dakota, city in Sargent County, North Dakota, United States * Forman, West Virginia, unincorporated community in Grant County, West Virginia, United States * Forman Glacier between Mount Franke and Mount Cole, in the Queen Maud Mountains of Antarctica *Forman Park, in Syracuse, New York Surname: *A. G. Forman CBE (1910–1967), Chief of Naval Staff of the Ghana Navy * Al Forman (1928–2013), baseball umpire *Alexander A. Forman (1843–1922), American soldier in the American Civil War *Alison Forman (born 1969), Australian soccer player *Andrew Forman (1465–1521), Scottish diplomat and Archbishop *Arthur Forman (1850–1905), English schoolmaster and cricketer *Bill Forman (1886–1958), baseball player * Bruce Forman (born 1956), American jazz guitarist *Carol Forman (1918–1997), American actress *Charles William Forman (1821–1894), Presbyterian missionary in Pakistan *Christine Jones Forman, American astrophysicist *Craig Forman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weber Number
The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named after Moritz Weber (1871–1951). It can be thought of as a measure of the relative importance of the fluid's inertia compared to its surface tension. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles. Mathematical expression The Weber number may be written as: :\mathrm = \frac = \left( \frac \right) \frac = \frac where * C_\mathrm is the drag coefficient of the body cross-section. * \rho is the density of the fluid ( kg/ m3). * v is its velocity (m/ s). * l is its characteristic length, typically the droplet diameter (m). * \sigma is the surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divergence Theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region". The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to integration by parts. In two di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spray (liquid Drop)
A spray is a dynamic collection of drops dispersed in a gas. The process of forming a spray is known as atomization. A spray nozzle is the device used to generate a spray. The two main uses of sprays are to distribute material over a cross-section and to generate liquid surface area. There are thousands of applications in which sprays allow material to be used most efficiently. The spray characteristics required must be understood in order to select the most appropriate technology, optimal device and size. Formation Spray atomization can be formed by several methods. The most common method is through a spray nozzle which typically has a fluid passage that is acted upon by different mechanical forces that atomize the liquid. The first atomization nozzle was invented by Thomas A. DeVilbiss of Toledo, Ohio in the late 1800s His invention was bulb atomizer that used pressure to impinge upon a liquid, breaking the liquid into a fine mist. Spray formation has taken on several forms, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquid-propellant Rocket
A liquid-propellant rocket or liquid rocket utilizes a rocket engine that uses liquid rocket propellant, liquid propellants. Liquids are desirable because they have a reasonably high density and high Specific impulse, specific impulse (''I''sp). This allows the volume of the propellant tanks to be relatively low. It is also possible to use lightweight centrifugal turbopumps to pump the rocket propellant from the tanks into the combustion chamber, which means that the propellants can be kept under low pressure. This permits the use of low-mass propellant tanks that do not need to resist the high pressures needed to store significant amounts of gasses, resulting in a low mass ratio for the rocket. An inert gas stored in a tank at a high pressure is sometimes used instead of pumps in simpler small engines to force the propellants into the combustion chamber. These engines may have a higher mass ratio, but are usually more reliable, and are therefore used widely in satellites for orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoluchowski Coagulation Equation
In statistical physics, the Smoluchowski coagulation equation is a population balance equation introduced by Marian Smoluchowski in a seminal 1916 publication, describing the time evolution of the number density of particles as they coagulate (in this context "clumping together") to size ''x'' at time ''t''. Simultaneous coagulation (or aggregation) is encountered in processes involving polymerization, coalescence of aerosols, emulsication, flocculation. Equation The distribution of particle size changes in time according to the interrelation of all particles of the system. Therefore, the Smoluchowski coagulation equation is an integrodifferential equation of the particle-size distribution. In the case when the sizes of the coagulated particles are continuous variables, the equation involves an integral: : \frac=\frac\int^x_0K(x-y,y)n(x-y,t)n(y,t)\,dy - \int^\infty_0K(x,y)n(x,t)n(y,t)\,dy. If ''dy'' is interpreted as a discrete measure, i.e. when particles join in discrete s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Physics
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While the activation energy must be overcome to initiate combustion (e.g., using a lit match to light a fire), the heat from a flame may provide enough energy to make the reaction self-sustaining. Combustion is often a complicated sequence of elementary radical reactions. Solid fuels, such as wood and coal, first undergo endothermic pyrolysis to produce gaseous fuels whose combustion then supplies the heat required to produce more of them. Combustion is often hot enough that incandescent light in the form of either glowing or a flame is produced. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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