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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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An atom which has lost one electron would be: (1) Negatively charged () Positively charged (3) Electrically neutral (4) Carry double positive charge Ans: Elec
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give me assignment on force
Hookes Law Hooke's equation actually holds (to some extent) in several other situations whereas an elastic body is deformed, like as wind blowing on a tall building, a musician
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a car with an initial speed of 24.5 km/hr accelerates at a uniform rate of 0.98 m/s^2 for 5.6sec. find the final speed and displacement of the car during this time.
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