Problem 4.17 - Problem 4.17 [Difficulty: 2] Given: Control...

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Problem 4.17 [Difficulty: 2] Given: Control Volume with parabolic velocity distribution Find: Volume flow rate and momentum flux Solution: Apply the expressions for volume and momentum flux Governing equations: = A dA V Q r ( ) = A A d V V mf r r r ρ Assumption: (1) Incompressible flow For a linear velocity profile i R r u i u V ˆ 1 ˆ 2 max = = r and also i rdr A d ˆ 2 π = r For the volume flow rate: () = = = = = = 4 2 2 4 2 2 2 ˆ 2 ˆ 1 2 2 max 0 2 4 2 max 0 2 3 max 0 2 max R R u R r r u dy R r r u i rdr i R r u Q h R y R r 2 max 2 1 R u Q = The momentum flux is () + = + = + =
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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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