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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.
Organ pipes are the musical instruments which are used for making musical sound by blowing air into the line. Longitudinal stationary pulses are created on account of superimpositi
What is resultant force
Determine an expression for the current in the ring jumping ring demonstration, an electromagnet provides magnetic field of B=0.2 cos 377t tesla over a circle of radius 1.2cm
Arago spot (D.F.J. Arago) A bright spot which appears in the shadow of a uniform disc being backlit through monochromatic light emanating from a point source.
Q. While rummaging in her backpack for her cell phone, Sally's Mini-Cooper rear ends Joey's Suburban. Sally's car is totaled while the suburban is fine. If Sally's car hit the sub
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#questiImagine a small observer is positioned in front of the cork in your picture above. As the cork approaches, the observer measures the wavelength of the waves passing by. How
Example 1:How far in meters does light travel in one year? Solution: 299,792,458m x 31,557,600s =9.461 x 10 to the power of15 Question, while i understand the above, why can we
Describe the variation of the radius of bright fringe of Newton's rings with refractive index of the thin film enclosed between the glass plate and plan-convex lens when observed b
what is the reason of gravity?
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