Problem 5.70

# Problem 5.70 - (a An expression for in cylindrical...

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Unformatted text preview: (a) An expression for in cylindrical coordinates. (b) Show result is identical to Equations 5.12. Problem 5.70 [Difficulty: 4] Given: Definition of "del" operator in cylindrical coordinates, velocity vector V V Find: Solution: We will apply the velocity field to the del operator and simplify. z k r e r e r ˆ 1 ˆ ˆ Governing Equations: (Definition of "del" operator) k V e V e V V z r r ˆ ˆ ˆ (Velocity flow field) r r e e e e ˆ ˆ ˆ ˆ (Hints from footnote) V V Substituting using the governing equations yields: k V z V e V z V e V z V k V r V e V r V e V r V k V r V e V r V e V r V k V e V e V z V k V e V e V r V k V e V e V r V k V e V e V z V r V r V k V e V e V z k r e r e k V e V e V V V z z z r r z z r r z r r r r r z r r z z r r z...
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