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Biot Savart Gauss's Law-Fluid Mechanics-Lecture Notes

Lecture Notes, Fluid Mechanics

Post: July 22th, 2012
Description
This lecture handout was provided by Prof. Anirvan Khan at National Institute of Industrial Engineering for Fluid Mechanics. It includes: Guass, Straight, Wing, Constant, Winglets, Vortex, Law, Fluid, Biot, Savart, Lift
This lecture handout was provided by Prof. Anirvan Khan at National Institute of Industrial Engineering for Fluid Mechanics. It includes: Guass, Straight, Wing, Constant, Winglets, Vortex, Law, Fluid, Biot, Savart, Lift
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Contents
Lecture F06 Mud: 1. Which came first, Biot-Savart for E&M or for Fluids? (2 students) Not sure. Biot-Savart was first used for Fluids in the mid 1800’s by Helmholtz. 2. Is there some sort of Gauss’s Law for vortices to avoid doing the Biot-Savart integral? (1 student) Nope. Gotta deal with it as is. 3. How is V� = �/2�r for the straight 3-D vortex in the first example? (1 student) I’m not sure what you mean. Carrying out the Biot-Savart integral on the straight 3-D vortex produced V� = �/2�h, where h was the perpendicular distance from the vortex. This is the same as the 2-D result, except that r was replaced with h (following Anderson’s notation). 4. If the circulation is greatest at the tips, is the lift greatest at the tips also? (1 student) I think you’re confusing the circulation � with the wake vortex strength � = −d�/dy . The circulation � and hence L� = �V� � both go to zero at the tips. In contrast, � is typically maximum near..

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