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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.
Null experiment: An experiment that yields no result after being executed. Null experiments are just as meaningful as non-null experiments; if current theory determined an obs
An astronaut on a small planet wishes to measure the local value of g by timing pulses traveling down a wire which hasa large object suspended from it. Assume a wire of mass3.50
LAW OF CONSERVATION OF MOMENTUM. "The total linear momentum of an isolated system always constant" OR "If there is no external force ap
A baton twirler throws a spinning baton directly upward. As it goes up and returns to the twirler's hand, the baton turns through four revolutions. Ignoring air resistance and assu
What is quantisation of electric charge?
Astronaut Catch A question such as this includes momentum principles. In any example in that two objects collide and can be considered isolated from all other net forces and th
project work
#questionwho is albert einstein..
A converging thin lens has a focal length of 27 centimetres. An object is placed 9 centimetres from the lens. Where is the image of this object formed? Ans: The images of g
A bucket of water is suspended from a ?xed point by a rope. The bucket is set in motion and the system swings as a pendulum. Though, the bucket leaks and the water slowly ?ows
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