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Suppose Fluid (say, water) occupies a domain D and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let be the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.
Fick's law for diffusion states that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that .
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.
Determine the causality principle for the Klein- Gordon equation in one dimension. Deduce that the speed of propagation is at most c.
Unit Vectors A unit vector is a vector of unit length. A easy animation of unit vectors and vector addition. A unit vector is a vector of length 1, sometimes also called a dir
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The topic for the project is to study and do calculation in Rotating Biological Contactor although you may choose a different title for your report. The aim is to research how the
what will happen if gravity becomes zero?is it possible in earth?
what are the examples of accurate and precise
parsec: The unit of distance explained as the distance mentioned by an Earth-orbit parallax of 1 arc sec. It equals approximate 206 264 au, or about 3.086 x 10 16 m.
Some phenomenon based on scattering: (i) Sky looks blue because of scattering. (ii) At the starting time of sunrise or sunset sun looks reddish. (iii) Danger signals are
Two light rays will interfere constructively with maximum amplitude if the path difference between them is: a) one wavelength b) one-half wavelength c) one-qua
A block of metal which weighs 60 newtons in air and 40 newtons under water has a density, in kilograms per meter cubed, of: a) 1000 b) 3000 c) 5000 d) 7000
Vector Direction The significance of 'direction' could be seen in the dissimilarity among velocity and speed. In physics, speed is a pure scalar or something along with a magni
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