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

Prof, quality standards and expectations for bathymetric survey

quality standards and expectations for bathymetric survey

Ac input resistance in common emitter configuration, AC Input Resistance in...

AC Input Resistance in Common Emitter Configuration Ratio of change in base emitter  voltage  ( ? V BE )  to  the  resulting  change  in  base  current  ( ? I B )  at  cons

Temporal coherance, how can we conclude whether at some time interference w...

how can we conclude whether at some time interference will take place or not with the help of the concept of temporal coherence?

Working of functional units in ultrasonic pulse echo system, Explain about ...

Explain about the working of functional units in ultrasonic pulse echo system. The master timer by the electronic clock triggers the signal pulse generator at ordinary interval

Explanation of displacement, EXPLANATION: Displacement is a physical q...

EXPLANATION: Displacement is a physical quantity which defines the motion of a body from its starting position to its final position. It is a vector quantity and can be shown b

Evaluate the height to which the center of the baton travels, A baton twirl...

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

Determine two-wattmeter method of measurement, (a) Show that the total powe...

(a) Show that the total power in a 3-phase, 3-wire system using the two-wattmeter method of measurement is given by the sum of the wattmeter readings. Draw a connection diagram.

Compare the emf and the potential difference, Q. Compare the emf and the po...

Q. Compare the emf and the potential difference . Comparison of emf and potential difference 1. The difference of potentials among the two terminals of a cell in an open cir

Fiber optics manufacture and fiber optics system manufacture, What is the d...

What is the difference among a fiber optics manufacture and a fiber optics system manufacture? It is a question that would sound silly in other industries although not in this

Classifications of capacitors, The capacitors can be classified on the basi...

The capacitors can be classified on the basis of nature of value, type of dielectric material used and polarity. On the basis of nature of value: Fixed value capacitor

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