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Problem 6.119 - direction of the lift force remains...

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Problem 6.119 [Difficulty: 3] Open-Ended Problem Statement: Consider flow around a circular cylinder with freestream velocity from right to left and a counterclockwise free vortex. Show that the lift force on the cylinder can be expressed as F L = ρ U Γ , as illustrated in Example 6.12. Discussion: The only change in this flow from the flow of Example 6.12 is that the directions of the freestream velocity and the vortex are changed. This changes the sign of the freestream velocity from U to U and the sign of the vortex strength from K to K . Consequently the signs of both terms in the equation for lift are changed. Therefore the
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Unformatted text preview: direction of the lift force remains unchanged. The analysis of Example 6.12 shows that only the term involving the vortex strength contributes to the lift force. Therefore the expression for lift obtained with the changed freestream velocity and vortex strength is identical to that derived in Example 6.12. Thus the general solution of Example 6.12 holds for any orientation of the freestream and vortex velocities. For the present case, F L = − U Γ , as shown for the general case in Example 6.12....
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