ChapterV.PartII

ChapterV.PartII - Chapter V Part II Biot-Savart Law...

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Chapter V. Part II. Biot-Savart Law Velocity Induced by a semi-Infinite Line Vortex of Strength d Γ at a point P P Vortex of Strength d Γ Runs from x=0 to infinity Velocity at P = d Γ /(4 π r) X = 0 Plane Consider a semi-infinite vortex of strength that starts at x=0, and ends at x= + . Consider also a point P, located at x=0, at a distance r from this line vortex. According to a theorem known as Biot-Savart law, this vortex will induce a circumferential velocity at the point P equal to d Γ /4 π r. The above expression can be rigorously derived. Please see the text (Chapter 5, pages 320-323) if you wish to know how one can arrive at this expression. In the interest of time, we will assume that this is given, and proceed. Velocity induced at a point P on the lifting line due to a semi-infinite vortex of strength d Γ : Next, let us assume that this point P is on the lifting line itself, say at x=0, y=y 0 , and z=0. The vortex starts at x=0, y=y, z=0 and ends at x=+
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ChapterV.PartII - Chapter V Part II Biot-Savart Law...

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