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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.
Using an Optical Bench This applet permits users to simulate standard optic elements that is lens, mirror, dielectrics, sources, apertures and observe the ways in which light r
Gauss' law (K.F. Gauss): The electric flux by a closed surface is proportional to the algebraic sum of electric charges contained in that closed surface; in differential form,
For a very every case the moment of inertia of a one particle about an axis is given by, I = mr 2 Here, m is the mass of the particle and r its distance from the axis under
The I beam weighs 0.6kN/m and supports the load which is P33 kN as shown. The distance from the load to point B is P34 m. Determine the vertical support reactions at A and B. (A
a) Describe how capacitance of a capacitor depends on area, distance among the plates and on the dielectric material. b) Draw electric field lines of a (i) positive poin
A resistor of 8Ω is connected in parallel with one of 12Ω and the combination is connected in series with one of 4Ω. A p.d. of 10V is applied to the circuit. The 8Ω resistor
Can you explain coherent sources of light?
What is the equation of wavelength related with a moving particle?
Given the ratio of velocities of two light waves traveled in vacuum and having wave lengths 5000A o and 6000A o . Can you explain by working of diamonds sparkle?
Can you explain thermistor? Write short notes on back emf and internal resistance of a cell.
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