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A fluid element in a flow may experience acceleration even when the flow is steady because

  • A.Steady flow always implies changing density
  • B.Acceleration is impossible in any steady flow
  • C.Velocity varies from point to point along its path
  • D.The time derivative of velocity is never zero

Answer: C

Correct answer: Velocity varies from point to point along its path

Steady means the velocity at a fixed point does not change with time, not that a particle moving through the field keeps its velocity. Following the particle, the convective term \( (\mathbf{V}\cdot\nabla)\mathbf{V} \) accelerates it - which is exactly what happens to fluid speeding up through a venturi in a perfectly steady flow.

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