Problem 5.67

Problem 5.67 - Problem 5.67 Given Find Solution[Difficulty...

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Problem 5.67 [Difficulty: 4] Given: Steady, two-dimensional velocity field of Problem 5.56 Find: These results are identical to the accelerations calculated in Problem 5.56. Solution: We will apply the particle acceleration definition to the velocity field  t V V V Dt V D a p Governing Equation: (Particle Accleration) Assumptions: (1) Incompressible flow (2) Two-dimensional flow (3) Steady flow For the given flow, uA x and vA y Thus u p t f 1 d d Ax p Af 1 or df 1 f 1 Ad t Integrating from x 0 to f 1 yields: x 0 f 1 f 1 1 f 1 dl n f 1 x 0 At Solving for f 1 yields: f 1 t () x 0 e Similarly, we can find: v p t f 2 d d A y p A f 2 or df 2 f 2 A dt Integrating from y 0 to f 2 yields: f 2 t y 0 e A t In this problem, x 0 1 2 m and y 0 2m Knowing the final position, we can solve for the time required. To reach (1, 1): x 1.0 m tl n 2 () 1 s t 0.693 s y 1.0 m n 1 2 1 s t 0.693 s t 0.693 s
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