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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.
Area of a Circle As a Limit Describing that the area of a circle is a limit of the sum of the area of interior triangles as the number of triangles goes to infinity.
Why we are showing work done over a closed path is zero to prove that electrostatic forces are conservative
A helium atom is in a galaxy travelling at a speed of 4.89 x 10 6 m/s away from the Earth. An astronomer on Earth observes a frequency from the helium atom of 6.52 x 10 14 H
Q. When a radar gun utter the pitch is 90 miles per hour at what point in the balls travel to home plate is the radar gun measuring the velocity? Answer:- The measu
What is the upside down delta in the Schrodinger Equation?
Plastics are polymers, meaning they are made up of molecules from many different elements. By utilizing different combinations, new polymers are made that can be manipulated from m
The mass of a mol of proton and electron is: (1) 6.023x 10 23 g (2) 1.008g and 0.55mg (3) 9.1x 10 -28 kg (4) 2gm Ans: (2) 1.008g and 0.55mg
Explain electric flux. Write its S.I. units. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up and enhances in
The graph below shows a sequence of alpha and beta decays, labeled 1, 2, 3, and 4. Consult Table 30-1 as required. a) Which shows alpha decays, and which represen
According to their frequencies, waves are separated into three categories: (1) Audible or sound waves : Range 20 Hz to 20 KHz. These are formed by vibrating bodies like as voc
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