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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 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
Is it determined by acceleration or velocity? Force or momentum?
Human Eye: It is spherical in shape, diameter about 2.5 cm, having of three layers. a) Sclera b) Choroid
solve
Beat period : The time interval among two successive beats is called as beat period. Beat frequency : The number of beats given per second is called as beat frequency.
Do fibers have losses? Everything in the universe is inefficient. It means that while a measured amount of something enters in a system, less comes out than initially went in.
The ideal gas approximation: The given assumptions are suppose while defining an ideal gas: (i) The number of molecules in the gas is very huge. (ii) The volume V having the
when a billard ball hits another billarid ball then other ball is maving but striking ball also move some distance why
why newtons 2nd law is called the real law of motion?
What is a neutron? A neutron is a subatomic particle. Neutron is one of the building blocks of the atom. It has a mass of about 1.675 x 10-27 kg. Its spin is + 1/2 and that
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