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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.
Inertia in a pile of books Stack up a pile of books. Grasp hold of the single at the bottom of the pile and give it a quick jerk. Can you delete it without upsetting the whole
Neutron possesses: (1)Positive charge (2)Negative charge (3)No charge (4)All are correct Ans: (3)No charge
how to measure least count of the instruments?
Assignment in fluid motion
An atom has 26 electrons and its atomic weight is 56. The number of neutrons in the nucleus of the atom will be : (1) 26 (2) 30 (3) 36 (
Mach number (E. Mach): The ratio of the speed of an object in a provided medium to the speed of sound within that medium. Mach's principle (E. Mach; c. 1870) The inert
retardation?
Determine the zero-point energy of a harmonic oscillator havingof a particle of mass 2.33 x 10 -26 kg and force constant 155 N m -1 .
What is Crystal twinning Crystal twinning occurs when two divide crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of
Figure shows the magnetic circuit of a relay. When each of the air gaps are 1.5mm wide find the mmf required to produce a flux density of 0.75 T in the air gaps. Use the B-H cu
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