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Suppose a fluid (say, water) occupies a domain D ⊂ R3 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 Φ = - kΔ + uV.
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
in the absence of diffusion(k=0), this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.
Explain the term 'resistivity' and write its S. I . unit. Derive the expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time.
Moment of Inertia In this section we get formulae for determining the moment of inertia or second moment of a mass around an axis for several common physical shapes. The mome
a) Sketch the small-signal equivalent circuit for a field-effect transistor (FET) and explain how it can be deduced from the properties of the real device. b) Draw the circuit
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In optics what is intended by the expression "constructive interference." Answer: This is factual for any kind of waves. Any time you have coherent waves of the same kind
Hoop conjecture (K.S. Thorne, 1972): The conjecture (as still unproven, though there is substantial evidence to hold up it) that a nonspherically compressed, nonspherical obje
If the temperature in a room is 84 degrees at the floor what will it be at a 30 foot ceiling
How much work has to be completed in assembling three charged particles q1= 2 micro coulomb, q2= 3 micro coulomb and q3= 4 micro coulomb at the vertices of a equilateral triangle o
What is spontaneous emission? Explain in brief. Spontaneous emission: a. This is the process by that a light source as like an atom, molecule, nano-crystal or nucleus into a
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