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

Calculate the velocity , An object of mass 4 kg is moving on a smooth horiz...

An object of mass 4 kg is moving on a smooth horizontal surface with a velocity of 10 m/s in rightward direction. A horizontal force F which shows in the above figure was applied o

Resistance-per-length of the wire, Question: The resistance-per-length...

Question: The resistance-per-length of the wire is wire's resistivity. Answer: Resistivity has units of ohms per meter therefore as regards wire it is certainly natur

Explain causes of low power factor, Causes of Low power factor The majo...

Causes of Low power factor The major causes of low power factor in the electric supply system are as follows. Due to reactive load Most of the AC motors used in i

How much temperature copper constantan is used for measuring, Copper consta...

Copper constantan is used for measuring temperature up to (A) 1400 o C (B) 800 o C. (C) 1100 o C. (D) 400 o C.  Ans: Copper constantan is used for meas

Keplar''s law, 1st law -What is the significance of the second foci of the ...

1st law -What is the significance of the second foci of the elliptical orbit? 2nd law -if the speed of the planet changes,why donot we feel it?

Uncertainty principle, Uncertainty principle (W. Heisenberg; 1927): A ...

Uncertainty principle (W. Heisenberg; 1927): A principle, central to quantum mechanics, that states two complementary parameters (such as position & momentum, energy & time, o

Explain start-up current in the bulb, The cold filament resistance of a lig...

The cold filament resistance of a light bulb is 20.0). The bulb consumes 75 W when it is operating from a 120-V source. By what factor does the start-up current in the bulb

Calculate the total amount of energy transfer by heat, A rigid tank primari...

A rigid tank primarily contains 3 kg of air at 500 kPa, 290 K. The tank is connected by a valve to a piston-cylinder assembly oriented vertically and consisting of 0.05 m³ of air i

Reducing friction with pencils, Reducing friction with pencils Place ro...

Reducing friction with pencils Place round pencils under a heavy box. Join a string to the box and find the force required to move it across a table. Search the force needed to

Evaluate with the direction of polarization of the polarizer, A polarizer (...

A polarizer (Polarization) consists of long-chain polymers aligned in a preferred orientation. How does that orientation evaluate with the direction of polarization of the polarize

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