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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.
What is Eclipses? Sun is a luminous body while earth and moon are non-luminous bodies. Only those parts of moon on the light of sun falls is visible. Also sun is larger than, b
why is the resultant of 3 non-coplanar vector always non-zero?
Question As-per to the law of reflection the angle of reflection is equal to the angle of incidence. An angle is at all times an angular separation between two planes a direct
a) Amplitude : It is the main value of distance of the particle from its equilibrium position. b) Time period (T): Smallest time interval after which the oscillatory motion
Find Cp for any substance in terms of V, T, P and S. Hint: How is C p related to (∂s/∂T) p ?
RANGE OF PROJECTILE: "It is the horizontal distance covered by the projectile from the point of projection to the point where it returns to its level of projection".
what causes glow in fire
How to calculate n factor of disproportion reaction? Total number of electron change divided by no. of moles of reactant This is conventional method Total electron chan
I''m transmitting microwave radiation from antenna to satellite..so when radiation(photons) is transmitted,how they interact with the molecules in the atmosphere layer by layer..I
VELOCITY- TIME GRAPH: The graphs which represents the variation of velocity of an object with respect to time is known as velocity- time graph.
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