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Unformatted text preview: Fluids – Lecture 20 Notes 1. Airfoils – Detailed Look Reading: http://www.av8n.com/how/htm/ Sections 3.1–3.3 (optional) Airfoils – Detailed Look Flow curvature and pressure gradients The pressures acting on an airfoil are determined by the airfoil’s overall shape and the angle of attack. However, it’s useful to examine how local pressures are approximately affected by local geometry, and the surface curvature in particular. Consider a location near the airfoil surface, ignoring the thin boundary layer. The local ﬂow speed is V , the local streamline radius of curvature is R . Another equivalent way to define the curvature is κ = 1 /R = dθ/ds , where θ is the inclination angle of the surface or streamline, and s is the arc length. Positive κ is defined to be concave up as shown. s n θ R = κ −1 u v x y V V θ V local cartesian xy axes 6 6 n p To determine how the pressure varies normal to the surface, we align local xy axes tangent and normal to the surface, and employ the y-momentum equation, with the viscous forces neglected. ∂p ∂v ∂v = − ρu − ρv ∂y ∂x ∂y The Cartesian velocity components are related to the speed and the surface angle as follows....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05