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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.
An alternating voltage given by v=100sin240t volts is applied across a coil of resistance 32 and inductance 100mH. Verify (a) the circuit impedance, (b) the current flowing,
Two travelling sinusoidal waves are described by the wave functions Y 1 = 55.00 sin [π (4.00 x - 1200 t )] Y 2 =55.00 sin [π (4.00 x - 1200 t - 0.250)] Where x ,
Uses of Ultrasonics: 1. Ultrasonic are used in diagnosis of disease, physical therapy as surgical tool & industry. 2. They are used in sounding devices to calculate the dept
A section through a magnetic circuit of uniform cross-sectional area 2cm 2 is shown in Figure. The cast steel core has a mean length of 25cm. The air gap is 1mm wide and the
An electron is in a box of width 3*10^-10m.what are de broglies wavelength and magnitude of momentum of the electron if it is in A)n=1 level B)n=2 level C)n=3 level Ans) Use the
how would you describe the discoveries of Benjamin franklin, Robert millikan, cgarles-augastin de coulomb and Ernest ruthford?
Correction of short sightedness To remove this defect a convex lens is used in front of eye.
Light propagates as transverse EM rays. The magnitude of electric field is much larger as compared to magnitude of magnetic field. We generally prefer to define light as electric f
The proton and neutron are collectively called as: (1) Deutron (2) Positron (3) Meson (4) Nucleon Ans: (4) Nucleon
Uncertainty principle (W. Heisenberg; 1927): A principle, central to quantum mechanics, that states two complementary parameters (such as position & momentum, energy & time, o
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