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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.
Ergosphere The region about a rotating black hole, among the event horizon & the static limit, where rotational energy can be extracted through black hole.
my question is regarding value of pie whether its decimal value which has non-repeating nature goes to infinity or it ends at some place?
This is the virtue of a material resists flow of electric current. It should be as high as possible. When material is subjected to an electrical pressure then will always be a flow
I want a project on this topic for cbse board
Define the Momentum and Impulse. Momentum, p, is a measure of a car's motion. p = m v where p is momentum in kg-m/s, m is mass in kilograms and v is the velocity of the ca
why The magnitude of known potential difference must be greater than the value of unknown potential difference to be measured.
State Kirchhoff's rules of current distribution in an electrical network. Using these rules verify the value of the current in the electric circuit given below.
The nucleus of helium contains : (1)Four protons (2)Four neutrons (3)Two neutrons and two protons (4)Four protons and two electrons Ans: (3)Two neutrons and two prot
Define Two-Dipole Interaction? Two classical dipoles with dipole moments μ 1 and μ 2 are separated by a distance R so that only the orientation of the magnetic moments is fre
(i) It has of continuously varying wavelengths in a exact wavelength range. (ii) It is given by solids, liquids and highly compressed gases heated to high temperature. (iii)
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