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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.
The magnitude of a charge, q, is to be determined by transferring the charge equally to two pith balls. Each of the pith balls has a mass of m, and is suspended by an insulating th
The rate of flow of energy or particles across a given surface.
what are the v-i characteristics of schottky diode?
Q. What are the limitations of electron microscope? An electron microscope is operated merely in high vacuum. This prohibits the utilize of the microscope to study living organ
Two trains simultaneously leave the same train station at noon. One train travels north and the other travels south. The position-time graph or both trains is shown in the accompan
If you "bow" a string on a violin you hear a note with a frequency of 1020 Hz. If the length of the string is about 40cm, what is the "wave" on the string? Draw a diagram to show
An open barge has the dimensions 22x40x12m. If the bargeis made out of 4.0-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in f
Faraday's laws of electromagnetic induction (M. Faraday) Faraday's first law of electromagnetic induction An electromotive force is induced into a conductor while the m
An electron in a hydrogen atom makes a transition from E 3 to E 1 . How much energy does the atom lose?
Copper is completely miscible with (A) Nickel. (B) Gold. (C) Hydrogen. (D) Lead. Ans: Copper is completely miscible with gold.
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