Solutions7 - Problem 6.6 [3] Given: Velocity field Find:...

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Problem 6.6 [3] Given: Velocity field Find: Expressions for local, convective and total acceleration; evaluate at several points; evaluate pressure gradient Solution: The given data is A2 1 s = ω 1 1 s = ρ 2 kg m 3 = uA x sin 2 π ω t () = vA y sin 2 π ω t = Check for incompressible flow x u y v + 0 = Hence x u y v + A sin 2 π ω t A sin 2 π ω t = 0 = Incompressible flow The governing equation for acceleration is The local acceleration is then x - component t u 2 π A ω x cos 2 π ω t = y - component t v 2 π A ω y cos 2 π ω t = For the present steady, 2D flow, the convective acceleration is x - component u x u v y u + Ax sin 2 π ω t A sin 2 π ω t A y sin 2 π ω t 0 + = A 2 x sin 2 π ω t 2 = y - component u x v v y v + sin 2 π ω t 0 A y sin 2 π ω t A sin 2 π ω t + = A 2 y sin 2 π ω t 2 = The total acceleration is then x - component t u u x u + v y u + 2 π A
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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.

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Solutions7 - Problem 6.6 [3] Given: Velocity field Find:...

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