Derive the conservation law, Physics

Assignment Help:

Suppose a fluid (say, water) occupies a domain D ⊂ R3 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 677_Derive the conservation law1.pngbe 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.

1003_Derive the conservation law.png

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 Φ = - kΔ + uV.

Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:

1290_Derive the conservation law2.png

in the absence of diffusion(k=0), this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.


Related Discussions:- Derive the conservation law

Principles of radiation therapy, Principles of radiation therapy: The ...

Principles of radiation therapy: The basic principle of radiation therapy is to maximize damage to the tumor while minimizing damage to the normal tissue.Factors that determin

Draw a circuit diagram of a common emitter amplifier, Draw a circuit diagra...

Draw a circuit diagram of a common emitter amplifier by using n-p-n transistor. Show input and output voltages graphically. The current gain for common emitter amplifier is 59.

Explain avalanche breakdown, At high reverse voltage, due to high electric ...

At high reverse voltage, due to high electric field, the minorities charge carriers, while crossing the junction acquires very high velocities. A chain reaction is prepared, giving

How a pure semiconductor under ordinary conditions behaves, A pure semicond...

A pure semiconductor under ordinary conditions behaves like (A) A conductor.               (B) An insulator. (C) A magnetic material. (D) A ferro-electric material. A

What is the rate of acceleration of the block, A 1.25-kg box is being pulle...

A 1.25-kg box is being pulled across a level surface where μk is 0.80. If the string is suddenly cut, causing the applied force to immediately go to 0.0 N, what is the rate of

Acceleration, how many seconds dose it take an elevator to travel 373m if i...

how many seconds dose it take an elevator to travel 373m if it accelerates at 4.80 m/s^2 and has a velocity of 17.8m/s how much time does it take an elevator to travel 373 meters

Lagrange points, Lagrange points: Points within the vicinity of two ma...

Lagrange points: Points within the vicinity of two massive bodies (like the Earth and the Moon) where each others' respective gravities balance. There are five, labeled L1 to

Capacitor has an amount of charge q on it, What do we denote when we say th...

What do we denote when we say that a capacitor has an amount of charge Q on it? Answer: If we obtain the expression the charge on the capacitor too accurately the value is

Measure the ratio of power factor of the circuit, Given below are two elect...

Given below are two electric circuits A and B Measure the ratio of power factor of the circuit B to the power factor of circuit A.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd