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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.
1. A child pulls a toy car weighing 0.20 kg across a smooth floor by means of a string attached to it. If the string makes an angle of 60° to the floor and the child pulls with a f
What are the components of endoscope? An endoscope can consist of following components • A rigid or flexible tube • A light delivery system to clarify the organ or object
SHAPE MEMORY ALLOYS: A group of metallic materials that can return to some previously defined shape or size when subjected to the appropriate thermal producer. That is to say, s
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Figure shows the transfer characteristic for an n-p-n silicon transistor.When the base current is 2.5mA, Verify (a) the value of collector current, (b) the static value of
why it is not possible to charge one object by rubbing without charging another object by rubbing
The tree needs to fall uphill even though it is leaning downhill. The felling notch at O is sufficiently large so that the resisting moment at O is negligible. The trunk above po
Coanda effect The effect which indicates that a fluid tends to flow along a surface, instead of flow through free space.
The magnetic induction at a point 15 cm from a long straight wire carrying a current is 4 X 10 -6 T Compute the current. (J - 12) B = μ o I/2πa I = 2πa X B/μo Current I
The energy needed to ionize an atom is known as ionization energy. It is the energy needed to make the electron jump from the present orbit to the infinite orbit.
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