Classify the type of flow: Which of the following describes a steady but non-uniform flow scenario?

Introduction / Context:
Flow classification distinguishes whether properties vary with time (steady vs unsteady) and whether they vary in space along the streamline or cross-section (uniform vs non-uniform). Correct classification helps select appropriate equations and coefficients.

Given Data / Assumptions:

• Steady means ∂()/∂t = 0 at a fixed point.
• Uniform means spatial invariance along the flow direction (properties do not change with x).
• Constant discharge implies time-invariant volumetric flow rate Q.

Concept / Approach:
In a duct with changing cross-section, keeping Q constant forces the mean velocity to change with area A(x) because V = Q/A. Thus the flow is non-uniform (varies with position) but steady (no time variation).

Step-by-Step Solution:
Option (b): Expanding tube, Q = constant → V decreases with x → spatial variation present → non-uniform; Q constant → steady.Option (a): Decreasing rate over time → unsteady.Option (c): Increasing rate over time → unsteady and non-uniform.Option (d): Increasing rate over time → unsteady (even if geometry is uniform).Option (e): Reservoir emptying → unsteady outflow.

Verification / Alternative check:
For (b), continuity gives dV/dx ≠ 0 with dV/dt = 0, which is the definition of steady, non-uniform flow.

Why Other Options Are Wrong:
(a), (c), (d), (e) all involve time variation of Q or head → unsteady.

Common Pitfalls:

• Equating “uniform” with “constant Q”. Uniform refers to spatial uniformity, not discharge alone.
• Ignoring geometry changes when assessing uniformity.

Final Answer:
An expanding tube carrying a constant discharge rate