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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 person attempts to calculate the gravitational constant G by suspending two 100.0kg spherical masses from a high ceiling in a shopping mall and calculating the deflection of the
Eddington limit (Sir A. Eddington) The theoretical limit on which the photon pressure would go above the gravitational attraction of light-emitting body. i.e., a body emitting
Define the use of quartz crystal method to detect ultrasonic waves. Quartz crystal method: This method is based onto the principle of Piezo-electric effect. While one pair o
A rod follower AB is subjected to a vertical up and down movement while resting on a circular contour of radius 30cm of a cam.the cam moves to the right with a velocity of 5 cm/s a
What is the cause of Brownian motion? Molecules in a gas move constantly, freely, randomly, in all directions and at high speeds. They are able to do so because the intermolecu
An imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be at that point.It is a point where the gravi
Whatn is Fusion
if CPH has mass, so CPH Theory is able explain the universe future. Universe should collapse. And it is able explain dark matter too. Am I wrong? Answer; you are correct that C
Derive the equation of uniformly acceleration motion by analytical method.
NEWTON'S SECOND LAW OF MOTION: This law states that "A force applied on body produce acceleration in its own direction. The acceleration differs directly with the applied force
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