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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.
Specified the expression below valid for points in the x-y plane what is the y-component of the electric field valid for points on the y-axis?
why flashlight suddenly become dim or bright when shaked?
Object A attracts object B with a gravatational force of 10 newtons from a given distance. If the distance between the two objects is doubled, what is the changed force of attracti
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assignment complete the following table
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Define Frozen Solid (Moscow Phys-Tech)? Evaluation how long it will take for a small pond of average depth D=0.5 m to freeze entirely in a very cold winter, when the
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sensitivity of moving coil galvanometer can be increased by decreasing?
project of class12,,to demonstrate electrostatics shielding
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