f06_mud_0304 - Lecture F06 Mud 1 Which came rst Biot-Savart...

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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 the tips.
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