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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.
State concept of Charging by conducting Charging by conducting - transfer of charge among two objects through contact - objects have similar charge
Longitudinal Waves and Guitar Strings According to the diagram this pressure wave consists of rarefactions and compressions. The compressions are regions of high pressure, wher
What are the merits of typical ultrasonic flaw detector? Merits of typical ultrasonic flaw detector: a. Particularly one side of the specimen is needed for the study. b.
definition and explanation
Q. State Huygen's principle. Huygen's principle: (a) Every point on a specified wave front may be considered as a source of secondary wavelets which spread out with the sp
These are resistors with long term stability and close tolerances. These are used in measuring instruments. Wire wound resistors, produced with long term stabilities and with speci
The mass of a string is 4.20 x 10 -3 kg, and it is stretched so the tension in it is 135 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength o
E lectrons have very much smaller mass than that of ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at extremely high frequencie
Define about the Bell Jar? A vessel with a small hole of diameter d in it is delegate inside a high-vacuum chamber. The pressure is so low that the signify free path λ>> d.
CO has same electrons as or the ion that is isoelectronic with CO is: (1) N + 2 (b) CN - (3) O + 2 (4) O - 2
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