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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.
Fusion Reaction: In nuclear fusion light nuclei are brought together to form a relation heavier nucleus. They energy free in nuclear fusion is larger than that free in fission.
12 joule of work has to be completed against an existing electric field to take a charge of 0.01 C from A and B. How much is the potential difference VB-VA.
EXAMPLES: (i) When the book is lying on a table, it exerts a downward force on the table (because of its weight). This force is known as action. The table exerts an upward forc
A particle is projected from ground with velocity 40sqrt2m/s.find- a)velocity and b)displacement of particle after 2sec .Take g=10m/s^2 Ans) velocity v=u+at a=-g v=40√2-10*2
Q. What is the dissimilarity between isolation transformers and step up or step down transformer? Answer:- In fact an isolation transformer may be physically the same as a
Write a mathematical expression for deviation produced by a thin prism and illustrate the terms.
The position of an airplane as a function of time is shown in the figure below. a. What is the average velocity of the airplane? b. What is the average speed of the air
At serve, a tennis player aims to hit the ball horizontally. What minimum speed is required for the ball to clear the 0.90 m high net about 15.0 m from the server if the ball is “
Draw the phasor diagram for an ideal transformer on no-load. (a) A 500 V/100V, single-phase transformer takes a full load primary current of 4A. Neglecting losses, Verify
a. Measure the force among two linear, parallel, long conductors carrying currents in opposite direction. b. Measure self inductances and mutual inductances among two co-axial s
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