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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.
A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the breaks, causing a suitcase to come flying towards he from the front of the bus. If
Kinetic and potential energy: Energy can exist in of 2 main forms. Kineti c energy is the kind of energy you probably think of right away when you imagine the energy. A pers
Q. What is ionisation potential energy? For hydrogen atom the energy necessary to remove an electron from first orbit to its outermost orbit (n=∞) is 13.6-0 = 13.6eV. This ene
Fast neutrons can be changed into slow neutrons by certain materials known as moderator's when last moving neutrons pass by a moderator, they combine with the molecules of the mod
A roller coaster starts from rest at the top of an 18m hill. The car travels to the bottom of the hill and continues up the next hill that is 10.0m high. How fast is the car moving
A steam bath An evaporating dish and steam bath can be contrived from a saucer and a tin. Scallops are cut out of the top of the tin to permit the steam to escape
A compound microscope with an objective of 1.0 cm focal length and an eye-piece of 2.0 cm focal length has a tube length of 20 cm. Measure the magnifying power of the microscope, i
When we move from a positive charge towards an equal negative charge along the line joining the two then initially potential reduces in magnitude and at centre changes into zero, b
An atom has 26 electrons and its atomic weight is 56. The number of neutrons in the nucleus of the atom will be : (1) 26 (2) 30 (3) 36 (
Watt; W (after J. Watt, 1736-1819): The derived SI unit of power, explained as a power of 1 J acting onto a period of 1 s; thus it has units of J/s.
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