ANS:C - expanding tube at increasing rate.

Unsteady non-uniform flow is typically represented by flow through an expanding tube at increasing rate.

Explanation:

1. Unsteady Flow:
   • Unsteady flow refers to flow conditions where the velocity and/or flow rate change with time at a given point in the flow field. This can occur due to changes in boundary conditions, sudden changes in flow rate, or variations in the geometry of the flow path.
2. Non-uniform Flow:
   • Non-uniform flow means that the velocity or flow rate varies across different sections of the flow path. This can occur due to changes in cross-sectional area, friction losses, or other factors affecting flow distribution.
3. Representative Scenarios:
   • Long pipe at constant rate: In this scenario, flow may be steady (not changing with time) and uniform (same velocity profile across the cross-section) if conditions do not change along the length of the pipe.
   • Long pipe at decreasing rate: This could imply a scenario where flow rate or velocity decreases along the length of the pipe, which could indicate non-uniform flow but not necessarily unsteady flow unless the change is with time.
   • Expanding tube at increasing rate: Flow through an expanding tube where the cross-sectional area increases along the flow direction can lead to both unsteady and non-uniform flow. The increasing cross-sectional area typically causes acceleration of flow, leading to changes in velocity with time (unsteady) and variations in velocity across the section (non-uniform).
   • Expanding tube at constant rate: This scenario would likely result in steady flow conditions if the rate of expansion does not change with time. However, it would still exhibit non-uniform flow due to the changing cross-sectional area.
4. Conclusion:
   • Among the options provided, flow through an expanding tube at increasing rate best represents unsteady non-uniform flow. The expansion causes changes in flow velocity both along the tube (unsteady) and across the tube's cross-section (non-uniform).