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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.
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Determine the angle of incidence for a ray of light to have minimum deviation of 39040' in equilateral prism.
The superposition theorem is a very useful network theorem. Write its statement
'To and Fro' type of motion is known as an Oscillatory Motion. It needed not be periodic and needed not have fixed extreme positions. The force/torque acting in oscillatory moti
What is electric field and formula for electric field is?
Any rigid body suspended from a fixed support constitutes a physical pendulum. Let Consider the situation when the body is displaced by a small angle Torque on the body about O is
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