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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.
Q. Write any three medical applications of laser. Medical applications (i) In medicine micro surgery has befall possible due to narrow angular spread of the laser beam.
The Doppler Effect shows that the spectrum of light from a visible body moving AWAY from the Earth will experience a shift in frequency when viewed from Earth. This definite s
Electric field lines In good metallic conductors: In good metallic conductors: (i) Static electric fields are not there (zero inside a conductor) (ii) Charges reside
We can produce energy from dynamic Casimir effect?
Some experiments with soap films Make the following forms from wire. Dip the several forms in the thick soap solution and view the films. Dip the wire form with the slider i
for assignment.
RESISTIVITY: R esistance may be defined as that property of a substance which opposes (or restricts) the flow of current (or electrons) through it. The practical as well as MK
binding energy of nucleas
electric field
One would expect proton to have very large: (1) Ionization potential (2) Radius (3) Charge (4) Hydration energy Ans:(4) Hydration energy
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