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Unformatted text preview: MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Review: Bernoulli Equation and Examples Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk LECTURE OUTLINE Review of Eulers Equation Eulers equation for incompressible flow Bernoullis Equation Review of Basic Aerodynamics How does an airfoil or wing generate lift? What are effects of viscosity? Why does an airfoil stall? Why are golf balls dimpled? WHAT DOES EULERS EQUATION TELL US? Eulers Equation (Differential Equation) Relates changes in momentum to changes in force ( momentum equation ) Relates a change in pressure (dp) to a chance in velocity (dV) Assumptions we made: Steady flow Neglected friction (inviscid flow), body forces, and external forces dp and dV are of opposite sign IF dp increases dV decreases flow slows down IF dp decreases dV increases flow speeds up Valid for Incompressible and Compressible flows Valid for Irrotational and Rotational flows VdV dp  = INVISCID FLOW ALONG STREAMLINES 2 2 2 1 2 2 1 2 2 1 2 1 =  + = + = + V V p p VdV dp VdV dp V V p p Relate p 1 and V 1 at point 1 to p 2 and V 2 at point 2 Integrate Eulers equation from point 1 to point 2 taking =constant BERNOULLIS EQUATION = + + = + 2 2 2 2 2 1 1 2 2 2 V p V p V p If flow is irrotational p+ V 2 = constant everywhere Remember: Bernoullis equation holds only for inviscid (frictionless) and incompressible ( =constant) flows Relates properties between different points along a streamline or entire flow field if irrotational For a compressible flow Eulers equation must be used ( is a variable) Both Eulers and Bernoullis equations are expressions of F =m a expressed in a useful form for fluid flows and aerodynamics Constant along a streamline HOW DOES AN AIRFOIL GENERATE LIFT? Lift is mainly due to imbalance of pressure distribution over the top and bottom surfaces of airfoil If pressure is lower than pressure on bottom surface, lift is generated Why is pressure lower on top surface? We can understand answer from basic physics Continuity Newtons 2 nd law HOW DOES AN AIRFOIL GENERATE LIFT? 1. Flow velocity over the top of airfoil is faster than over bottom surface Streamtube A senses upper portion of airfoil as an obstruction Streamtube A is squashed to smaller crosssectional area Mass continuity AV=constant, velocity must increase Streamtube A is squashed most in nose region (ahead of maximum thickness) A B HOW DOES AN AIRFOIL GENERATE LIFT?...
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This note was uploaded on 02/11/2012 for the course MAE 3241 taught by Professor Staff during the Spring '11 term at FIT.
 Spring '11
 Staff

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