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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.
Define coherence and explain temporal and spatial coherence. Show that visibility is a maxim of coherence. Define the 'Q' factor for a spectral line. Explain coherence length and c
Does upthrust change in different liquids (examples please)
The overall length of a particular wind instrument is 35.0 cm. The resonating air column vibrates as ina pipe that is open at both ends. (a) Find the frequency of the lowest not
Illustrate a labelled diagram of Hertz's experimental set-up to produce electromagnetic waves. Describe the generation of- electromagnetic waves using this set-up.
a ball is dropped from a bridge 122.5m high. after the ball has been falling for2 sec another is thrown straight downwards after it. the initial velocity of the ball is such that
The minimum real charge on any particle which can exist is: (1)1.6x 10 -19 coulomb (2) 1.6x 10 -10 coulomb (3)4.8 x 10 -10 coulomb (4)Zero Ans: (1)1.6x 10 -19 c
Show the types of chromatic aberration. What do you understand by Fraunhoffer lines? Explain their origin.
4 dimenestional motion examples
Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit
A bird flies in the east direction with a speed of 5 ms -1 . The wind is blowing towards north at a speed of 3 ms -1 . Determine the relative velocity of the bird with
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