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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.
(i) The size examines cannot be operated to derive relations other than product of power functions, for example, s = ut + 1/2 at 2 or y = y 0 cosωt and so on, cannot be derived
which circular path in any time in any mation
Object-Image Relationships Ray tracing for a thin lens showing the formation of a real image of an object.
In whole analog to the work energy theorem for the translator motion, it might be stated for rotational motion as: Δ W rot = K rot The net rotational work given by the force
Explain about the term step index fibre. Step index fibre: Into a step index fibre, the refractive index keeps constant throughout the core and decreases at the core-claddin
At 200.0 K, silicon has 1.89 x 10 5 thermally liberated charge carriers/cm 3 . If it is doped with 1 As atom to 3.75 million Si atoms, what is the ratio of doped carriers to t
Are heat fuses necessary? The working temperature range of the fiber optics ordinary end is critical if the performance of the system is to be kept and the life guaranteed. A
Q. What are the conditions to achieve the laser action? Conditions to achieve laser action (i) There should be an inverted population that is more atoms in the excited
Determine the highest order spectrum which can be seen with monochromatic light of 589.3 nm wavelength by means of a diffraction grating having 15000 lines/inch.
Q. Define the unit of self inductance. One henry is described as the self-inductance of a coil in which a change in current of one ampere per second produces an opposing emf of
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