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posted by  Boilermaker on 11/4/2009 9:20:14 PM  |  status: Live  |  Earned Karma: 47

Fluid Mechancis - Vortex Filaments, Biot-Savart Law

Course Textbook Chapter Problem Needs by
Fluid Mechanics Fundamentals of Aerodynamics 5.2 N/A 11/5/2009 at 11:00:00 PM
Question Details:
Consider a straight vortex filament of finite length and vortex strength (Gamma) per unit length. We define the x-axis coincident with the vortex filament, as shown below. Then, any distance normal to the filament can be described by the y-coordinate. This makes a two dimensional problem. There is no free-stream velocity in this problem. The region of interest of the vortex filament extends from x=x1 to x=x2.

1.Solve for the induced velocity at the point P(x,y) in a manner that is valid for all x and y.
2. What is the velocity for the x ---> ∞ and y>0.
3. What is the velocity for the x=0 and x=x1 planes for x2 ---> ∞.



This is what I have:

V = in the z-direction

V =
s1 = x-x1
s2 = x-x2
s = x-
ds = -d
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