Examples of Steady Flow Phenomena in Physics and Asymptotic Processes
Explore examples of steady flow phenomena in physics involving Ohm's law, Fourier's law, and more. Discover how processes approach end points asymptotically, such as in radioactive decay and cooling of objects. Gain insights into modeling and solving these phenomena.
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Presentation Transcript
Tutorial-0 Q1: Give examples of phenomenon in Physics involving Steady Flow? How to formulate the model there? Solve? Q2: Give examples of phenomenon where process approaches an end point asymptotically?
Steady Flow Sink Source
Examples: Steady Flow ?? ??= ? (?? ??) Electricity Ohm s law ?? ??= ?(?? ??) Heat Fourier s law ?? ??= ?(?? ??) Hagen-Poiseuille law Fluid ?? ??= ?(?? ??) Brownian Diffusion Diffusion Does this point to an underlying generality of the phenomenon of flowing? Additional Question: Dimensions of G, K, ?, C ?
Steady Flow ?? ??= ? (?? ??) Something which flows Cause of flow ?? ??= ?(?? ??) ?? ??= ?(?? ??) ? ? ??= ?? ??= ?(?? ??) Intuition demystified!
Processes where rate becomes less and less over time Emptying of a Water Tank Discharging of a Capacitor Radioactive Decay Cooling of a warm object
Emptying of a Water Tank ??? ?? ??= ?(?? ???) ???,??= ???+ ??? ?0 ? As, ?=??, d?/dt =? d?/dt ?? ??= ??? ??= ???? ?? ??? ?? ??= ???? ?? = ??? ?? ? ? ? ??? = ??? ???????????, ? + ? ? ??? = ??? At t = 0, ? = ?0 , therefore, C =???? ? = ??? ??? Finally, ? ?? ? ?? ? = ?? ? ?is called the flow conductance
Emptying of a Water Tank ??? ? = ??? ??? ?? ?0 ?0 ? Water level, ? ?? ??? Time, ? Exponential Decay : relaxation time As t , ? ? At t = A/??g = , ? =? ??0 At t = ? , ? = (? ?)? ?0
Processes where rate becomes less and less over time Emptying of a Water Tank Discharging of a Capacitor ?? ??= ???? ?? ??= ? ? ??? ? = ?? ? ?is flow conductance = RC discharge time constant Radioactive Decay Cooling of a warm object ?? ??= ?? ?? ??= ?(? ??) ? depends on size, shape, specific heat, surface condition of an object, etc. is decay rate t1/2 =
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