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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 river is flowing 4.0 m/s to the east. A boater on the south shore plans to reach a dock on the north shore 30.0° downriver by heading directly across the river. a. What shoul
INSTANTANEOUS VELOCITY: The velocity of a body at a certain instant of time is known as instantaneous velocity.
a) Sketch an IV characteristic of a photodiode, showing how the curve shifts as a result of the illumination intensity incident on the device being varied. b) Indicate on the c
an object moves from postion +16m to the postion +47m in 12s.what is its total displacement and its average velocity?
Which Is Best Tan A position Or Tan B Position.?
Explain Simple Harmonic Motion Many repeating motion problems can be solved by taking the displacement as where d is distance in meters, A is amplitude in meters,
Explain Independence of Vectors Quantities Perpendicular vector quantities are independent of one another. This means that the actions of one vector will not affect the action
P r oblem Solving Technique There are two approaches to solve a problem. They are:- 1. Top down -A top down design approach starts by identifying the major components
sensitivity of moving coil galvanometer can be increased by decreasing?
(i) Time section of vibration of particle is described as the time taken by the particle to complete single vibration about its mean position. (ii) It is the time given by the r
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