3241 Lecture 3

3241 Lecture 3 - MAE 3241 AERODYNAMICS AND FLIGHT MECHANICS...

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MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Views of Motion: Eulerian and Lagrangian Conservation Equation Summary January 19, 2011 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk
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KINEMATIC PROPERTIES: TWO ‘VIEWS’ OF MOTION 1. Lagrangian Description Follow individual particle trajectories Choice in solid mechanics Control mass analyses Mass, momentum, and energy usually formulated for particles or systems of fixed identity ex., F =d/dt(m V ) is Lagrangian in nature 1. Eulerian Description Study field as a function of position and time; not follow any specific particle paths Usually choice in fluid mechanics Control volume analyses Eulerian velocity vector field: Knowing scalars u, v, w as f (x,y,z,t) is a solution ( 29 ( 29 ( 29 ( 29 ( 29 k t z y x w j t z y x v i t z y x u t z y x V t r V ˆ , , , ˆ , , , ˆ , , , , , , , + + = =
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CONSERVATION OF MASS This is a single scalar equation Velocity doted with normal unit vector results in a scalar
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3241 Lecture 3 - MAE 3241 AERODYNAMICS AND FLIGHT MECHANICS...

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