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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 particle with mass m = 2:5 is moving along a straight trajectory. The distance covered by a particle is described by the function S(t) = t 3 + 2t 2 , where t > 0 is the time
What is electric field and formula for electric field is?
calculate the frequency of radiation which must be incident on a substance placed in magnetic field strength so that the electron can absorb energy
what is expansion of solids
State perpendicular axis theorem. a) Explain impulse-momentum principle. b) Verify the equation of motion for translation
Q When calculate Planck's constant, a student's calculations produce values of 5.78 × 10 -34 J·s and 7.29 × 10 -34 J·s. If the accepted value is 6.63 × 10 -34 J·s, what is
Amplitude: The maximum displacement of a body on either side of the mean position during simple harmonic motion is known as amplitude and it is shown by x.
On transitory from a medium with one index of refraction to a medium with a different index of refraction light is typically both reflected and refracted. Under some conditions how
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Draw and discuss volt-ampere characteristics of a tunnel diode. Ans: Volt-ampere characteristics of a tunnel diode: The V-I characteristics of a tunnel diode are shown in fi
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