lect_22 - Potential Flow Formulation Velocity v =...

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Unformatted text preview: Potential Flow Formulation Velocity v = Vri> Governing Equations for P-Flow (a) Continuity 1 (b) Bernoulli for P-Flow (steady or unsteady) p =-p 1 ~ 4 1 ~ + gy Boundary Conditions for P- Flow Types of Boundary Conditions: (c) KinematicBoundary Conditions- specifythe flowvelocity Gat boundaries. - 94 -- Un an ( f t + 5 1 ( ~ 4 ) ' + gy + C (t) (prescribed) Linear Superposition for Potential Flow In the absence of dynamic boundary conditions, the potential flow boundary value problem is linear. Potential function d>, Linear Superposition: if 4 ' 2 , . + . are harmonic functions, i.e., v2#, = 0, then # = y^aj#j, where a, are constants, are also harmonic, and the solution for the boundary value problem provided the kinematic boundary conditions are satisfied, i.e., The key is to combine known solution of the Laplace equation in such a way as t o satisfy the kinematic boundary conditions (KBC) . Laplace Equation in Different Coordinate Systems Cartesian ( X ) Z J , Z ) Cylindrical (r, 0, Z ) Spherical ( r ) 0) 9) -- Simple Potential Flows 1. .Uniforrn_Stream V2 (ax + by + cz + d)...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.29 taught by Professor Henrikschmidt during the Spring '07 term at MIT.

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lect_22 - Potential Flow Formulation Velocity v =...

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