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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.
what is linear and angular variables?
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Explain the term poly elastic and give some of example.
The specific resistance of copper is 1.7ohm. find the resistance of copper wire of length 10m and diameter 1mm. solution) R=ρ*l/A so ou have ρ,l and r(radius). you can use the f
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Since polymeric materials can be formed in thin, highly uniform and non porous films with high dielectric strength, these materials are preferred dielectric materials for capacitor
Instructors Own Problem: 1) On the surface of some strange planet, Mr. Spock finds his weight to be1200N. He then goes 5000km above the surface, and finds his weight to be on
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