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Unformatted text preview: Fluids – Lecture 1 Notes 1. Formation of Lifting Flow Reading: Anderson 4.5 – 4.6 Formation of Lifting Flow Conservation of Circulation — Kelvin’s Theorem The circulation about any closed circuit is defined to be vector ˆ Γ ≡ − V · dvectors = − ξ vector · n dA where dvectors is an arc length element of the circuit, and vector V is the local ﬂow velocity. The equivalent vorticity area integral form follows from Stokes Theorem. In 2-D, this second form is Γ = − ξ dA (In 2-D) To investigate the formation of a lifting ﬂow about an airfoil, we now consider the circulation Γ about a circuit demarked by ﬂuid elements which are drifting with the ﬂow (a fine smoke ring would constitute such a circuit). Because both the shape of the circuit and the velocities V ds ξ dA seen by the circuit will in general change in time, there is the possibility that Γ( t ) will change in time as well. The rate of change of this circulation is d Γ d D = − ξ dA = − ( ξ dA )...
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- Fall '05
- Fluid Dynamics, Lift, Airfoil, Kelvin’s Circulation Theorem