Problem 5.40 - Problem 5.40[Difficulty 2 The velocity field...

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Problem 5.40 [Difficulty: 2] Given: The velocity field provided above Find: (a) the number of dimensions of the flow (b) if this describes a possible incompressible flow (c) the acceleration of a fluid particle at point (2,1,3) 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) Steady flow (velocity is not a function of t) Since the velocity is a function of x, y, and z, we may state that: The flow is three dimensional. 0 z w y v x u Based on assumptions (1) and (2), the continuity equation reduces to: This is the criterion against which we will check the flow field. 0
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