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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.
Figure shows the frequency spectrum of a signal at 1184kHz displayed by a high-speed virtual DSO. Determine (a) The harmonic relationship among the signals marked 'o' and 'x',
As seen from above, a playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars o
Visible Radiation (Waves): Visible waves have a wavelength range among 400 and 700 nanometre.
what is moment of Inertia? Give an example, I need some specific and unique examples of moment of interia topic.
Explain corrosion This corrosion can happen either when a conducting liquid is in contact with a metal or when two dissimilar metals /alloys are is partially immersed in a con
Force in Two and Three Dimensions - Pressure and Fluids Pressure is a force exerted over an area and is measured in Pascals (Pa). P (in Pa) = Force (in newtons) / area (
Q. A Plano-convex lens of radius 3 m is placed on a flat glass plate and is illuminated by monochromatic light. The radius of the 8th dark ring is 3.6 mm. Calculate the wavelength
Cathode rays are : (1)Protons (2)Electrons (3)Neutrons (4)alfa -particles Ans; (2)Electrons
Question: Regard as a high school built to handle 1500 students but attended by 2500 students. Between classes the halls are crowded with students moving to their next class. A
1 Coulumb Charges: 1 coulumb charge is that amount of charge which when placed 1 m from an identical charge in vacuum which repels it with a force of 8.99 × 109 N.
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