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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.
Does a piece of glass reflect more light than a piece of paper?
Classical free electron theory: The free electron theory of metals using classical laws was developed by Dude and Lorentz in the beginning of last century. That time the va
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A scooterist is racing at a speed of 72 km per hour. If the radius of the wheel is 20 cm, find the angular speed of the wheels. Ans) 72kmph=20m/s 20cm=0.2m; v=rw w=v/r w=20/0
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define electrostatistic
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