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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.
how to standing waves formed in closed pipes
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In the circuit shown below, a potentiometer is used to vary the current to the lamp. If the only resistance is due to the lamp, what is the current in the circuit?
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what are characteristics of simple harmonic motion
What is an alloy? An alloy is a homogeneous hybrid of two or more elements, at least one of which is a metal, and where the resulting material has metallic properties. The resu
measurement and calculation with formula
The potential difference across the terminals of a cell when it is not supplying any current is known as it's emf.
Conductor: Conductors are those substances which permit electric current to passes easily by them. e.g. Metal, impure, water etc.
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