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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.
Hubble constant; H0 (E.P. Hubble; 1925): The constant that determines the relationship among the distance to a galaxy and its velocity of recession because of the expansion of
Besides solid, liquid, and gas, what is the fourth form of matter? Ans: The fourth form of matter is plasma.
your dog is running around the grass in your back yard. He undergoes successive displacements 3.50 m south, 8.20 m northeast, and 15.0 m west. What is the resultant displacement. h
If the charges are situated in a medium of permittivity ε, then the magnitude of the force between them will be, If the charges are situated in a medium of permittivity ε, then th
INERTIAL FRAME OF REFERENCE: "A frame of reference which is not being accelerated and it might be at rest or moving with uniform velocity is known as inertial frame of referen
Explain about the monochromaticity of laser. Monochromaticity: The light emitted through a laser is monochromatic, that is this is of one wavelength (colour). Although in ca
A coil havingof a resistance of 100 and an inductance of 200mH. If an alternating voltage, v, givenby v=200sin500t volts is applied across the coil, measure (a) The circuit
A flat aluminum plate of 0.2 m thickness is initially at 120 Celsius. At time t=0, it is immersed in a liquid at 10 Celsius. Assume a very large heat transfer coefficient on both t
Explain physically how a p-n junction functions as a rectifier. Ans: When a P-N junction diode is forward-biased and applied voltage is increased from zero, hardly any current
Explain Ballast Volume Pressure? Two containers I and II prodigal with an ideal gas are connected by two small openings of the same area, A, through a ballast volume B. The tem
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