Problem 5.44

# Problem 5.44 - Problem 5.44 [Difficulty: 2] Given: Find:...

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Problem 5.44 [Difficulty: 2] Given: The 2-dimensional, incompressible velocity field provided above Find: (a) dimensions of the constant A (b) simplest x-component of the velocity (c) acceleration of a particle at (1,2) Solution: We will check the dimensions against the function definition, check the flow field against the continuity equation, and then apply the definition of acceleration.  0 t w z v y u x Governing Equations: (Continuity equation) t V z V w y V v x V u Dt V D a p (Particle acceleration) Assumptions: (1) Incompressible flow ( ρ is constant) (2) Two-dimensional flow (velocity is not a function of z) (3) Steady flow (velocity is not a function of t)  L L t L xy v A 1 1 Lt A 1 Since vA x y it follows that A v xy and the dimensions of A are given by: 0 y v x u x u Ax y v Based on the assumptions above, the continuity equation reduces to: Therefore: Integrating with respect to x will yield the x-component of velocity:
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## This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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