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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.
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In a single slit diffraction pattern the distance between the first minimum on left to first minimum on the right is 0.054 cm for a light of wavelength 5890 Å. Determine
Can ever the whole charge of a body be transferred
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The Coriolis effect is a deflection of moving objects when they are reflects in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the l
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Dielectric constant of vacuum is (A) Infinity. (B) 100. (C) One. (D) Zero. Ans: Dielectric constant of vacuum is one.
what is specific gravity
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