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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.
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
The wheatstone bridge: You have already solved resistor networks using Ohm's law and Kirchoff's laws. In this unit we are going to look at a special arrangement of series and
Dot Product A Easy demonstration of the relation among the dot product of 2 vectors and the angle among them. Move the slider to view the changes.
Q. Determine the elapsed time in kinematics? Let S = 1 + c 2 + c 4 + ........ Then, S = 1 + c 2 (1 + c 2 + c 4 +.......... ) S = 1 + c 2 S so, S - c 2 S = 1
The Broken Pencil-Ray Optics A general classroom demonstration includes placing a pencil (or similar object) within an upright position within a round glass of water. The penci
Is the common end is important? Even though manufacturers place extra attention on fibers and illuminators the common end is a very important piece for the correct operation of
Describe an actual situation that would give rise to the free body diagram
The force between two magnetic poles divided by a distance ‘d' in air is ‘F'. At what distance between them the force becomes doubled?
Which of the following isn't true of an electric field? Answer An electric field can as well as does exist in vacuum. Except for the one about vacuum the entire the answe
Q. A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15cm. Give the location of the image and the magnification. Describe what happens as the needle is moved
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