Problem 5.42

# Problem 5.42 - Problem 5.42 Given Find[Difficulty 2 The...

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Problem 5.42 [Difficulty: 2] Given: The velocity field provided above Find: (a) if this describes a possible incompressible flow (b) the acceleration of a fluid particle at point (x,y) = (0.5 m, 5 mm) (c) the slope of the streamline through that point Solution: We will check this flow field against the continuity equation, and then apply the definition of acceleration    0 t w z v y u x Governing Equations: (Continuity equation) t V z V w y V v x V u Dt V D a p (Particle acceleration) Assumptions: (1) Incompressible flow ( ρ is constant) (2) Two-dimensional flow (velocity is not a function of z) (3) Steady flow (velocity is not a function of t) 0 y v x u This is the criterion against which we will check the flow field. Based on the assumptions above, the continuity equation reduces to:

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Problem 5.42 - Problem 5.42 Given Find[Difficulty 2 The...

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