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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.
show that work is a path function not a property
The idea that everything is made up of very small particles has been developed over many years supported by several experiments: (i) Brownian motion :
Q. A twelve-slit strobe disc is rotated at the max stopping frequency for a vibrating object. The strobe is rotated at 4.0 Hz. (a) Evaluate the period of the vibrating object?
Keplers Second Law After studying a wealth of planetary data for the motion of the planets about the sun, Johannes Kepler reasons three laws of planetary motion. Kepler's secon
give a example
A bat emits a sound whose frequency is 142 kHz. The speed of sound in air at 20.0°C is 343 m/s. However, the air temperature is 35°C, so the speed of sound is not 343 m/s. Find the
Making a sun-dial To withstand all weather, a sun-dial should be form of metal or painted wood. A cardboard model can be formed for easy experiments. The gnomon which casts
A lever of the second class Use a uniform wooden bar about 1 m long, 4 cm wide and 5 mm thick. Drill a hole near single end, in the centre of the width dimension. Also drill a
Demonstrating the cause of difference in length of day and night in some places:- Use the similar apparatus as in 6 above. Mark a circle on the ball around its centre to show t
Gray; Gy (after L.H. Gray, 1905-1965): The derived SI unit of absorbed dose, described as the absorbed dose wherein the energy per unit mass imparted to the matter through ion
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