Flow Classification – Unsteady and Non-Uniform A flow through an expanding tube at an increasing rate with time is best described as which type of flow?

Introduction:
Flow can vary with time and space. The question tests whether the student can correctly classify a situation with both time variation and spatial variation.

Given Data / Assumptions:

• Expanding tube means cross-section varies with position.
• Rate of flow is increasing with time.

Concept / Approach:

Uniform vs non-uniform refers to spatial variation at a fixed time. Steady vs unsteady refers to time variation at a fixed point. An expanding tube creates spatial variation in velocity distribution, and an increasing discharge with time creates temporal variation.

Step-by-Step Solution:

Verification / Alternative check:

Continuity for incompressible flow, A(x) * V(x,t) = Q(t). If Q increases with time and A depends on x, then V depends on both x and t, confirming the classification.

Why Other Options Are Wrong:

Yes / No: These are not flow types and do not classify the physics.Steady uniform / Steady non-uniform: Both contradict the explicit time variation.

Common Pitfalls:

Assuming non-uniform automatically means unsteady. A diffuser with constant Q is non-uniform but steady; here Q is changing, so it is both.

Final Answer:

Unsteady and non-uniform flow