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Unformatted text preview: Problem 7.7 [ 2 ] Given: Equations Describing pipe flow Find: Non-dimensionalized equation; Dimensionless groups Solution: Nondimensionalizing the velocity, pressure, spatial measures, and time: L V t t L r r L x x p p p V u u = = = = = * * * * * Hence * * * * * t V L t r D r x L x p p p u V u = = = = = Substituting into the governing equation + + = = * * * 1 * * 1 * * 1 1 * * 2 2 2 r u r r u D V x p L p t u L V V t u The final dimensionless equation is + + = * * * 1 * * * * * * 2 2 2 r u r r u D L V D x p V p t u The dimensionless groups are D L V D V p 2 Problem 7.12 [ 2 ] Given: That speed of shallow waves depends on depth, density, gravity and surface tension Find: Dimensionless groups; Simplest form of V Solution: Apply the Buckingham procedure c V D g n = 5 parameters d Select primary dimensions M, L, t e...
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This note was uploaded on 08/25/2011 for the course AME 331 taught by Professor Zohar during the Fall '08 term at University of Arizona- Tucson.
- Fall '08