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Unformatted text preview: Fluids Lecture 4 Notes 1. Dimensional Analysis Buckingham Pi Theorem 2. Dynamic Similarity Mach and Reynolds Numbers Reading: Anderson 1.7 Dimensional Analysis Physical parameters A large number of physical parameters determine aerodynamic forces and moments. Specif- ically, the following parameters are involved in the production of lift. Parameter Symbol Units Lift per span L mt 2 Angle of attack Freestream velocity V lt 1 Freestream density ml 3 Freestream viscosity ml 1 t 1 Freestream speed of sound a lt 1 Size of body (e.g. chord) c l For an airfoil of a given shape, the lift per span in general will be a function of the remaining parameters in the above list. L = f ( , , V , c, , a ) (1) In this particular example, the functional statement has N = 7 parameters, expressed in a total of K = 3 units (mass m , length l , and time t ). Dimensionless Forms The Buckingham Pi Theorem states that this functional statement can be rescaled into an equivalent dimensionless statement 1 = f ( 2 , 3 . . . N K ) having only N K = 4 dimensionless parameters. These are called Pi products, since they are suitable products of the dimensional parameters. In the particular case of statement (1), suitable Pi products are: L 1 = 1 = c lift coecient 2...
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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