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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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Suppose a fluid (say, water) occupies a domain D ⊂ R 3 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
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The real length of path traversed by a body in a sub interval of time is called as distance. It is the real path travelled by an object among its final and initial positions. It is
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Net force acting on particle of mass 2 kg is 10N in north direction.At t=o, particle was moving eastwards with 10m/s. Find displacement and velocity of particle after 2 seconds.
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