GATE ME 2014 Set 4 — Question 24
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Fluid Mechanics → Fluid Kinematics & Dynamics → Local, Convective & Material Acceleration
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Question
A flow field which has only convective acceleration is
Correct answer
(C) a steady non-uniform flow
Solution
The total acceleration of a fluid particle is given by the material derivative of the velocity vector :The question asks for a flow field that has only convective acceleration. This implies two conditions:
1.The convective acceleration must be non-zero: .
2.The local acceleration must be zero: .
Let's analyze the given options:- Steady flow: A flow is steady if the fluid properties (like velocity) at any point in the flow field do not change with time. This means the local acceleration is zero, .
- Unsteady flow: A flow is unsteady if properties change with time at a point. This means the local acceleration is non-zero, .
- Uniform flow: A flow is uniform if the velocity vector is identical at every point in the flow field at any given instant. This means the velocity does not change with spatial coordinates, so the convective acceleration is zero, .
- Non-uniform flow: A flow is non-uniform if the velocity changes from point to point at any given instant. This means the convective acceleration is non-zero, .
- Steady (Local acceleration is zero).
- Uniform (Convective acceleration is zero).
- Total acceleration is zero. This is incorrect.
- Unsteady (Local acceleration is non-zero).
- Uniform (Convective acceleration is zero).
- This flow has only local acceleration. This is incorrect.
- Steady (Local acceleration is zero).
- Non-uniform (Convective acceleration is non-zero).
- This flow has only convective acceleration, which matches the condition. This is correct.
- Unsteady (Local acceleration is non-zero).
- Non-uniform (Convective acceleration is non-zero).
- This flow has both local and convective acceleration. This is incorrect.
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