Flow in varying-area conduits – classification for constant volumetric rate A liquid flows through an expanding tube (increasing cross-section) at a constant volumetric flow rate. How should this flow be classified?

Introduction:
Correctly labeling flows is essential before applying momentum and energy equations. The two attributes are time variation (steady vs unsteady) and spatial variation along the conduit (uniform vs non-uniform). An expanding tube at constant flow rate provides a classic example to test these definitions.

Given Data / Assumptions:

• Rigid tube with cross-sectional area increasing with downstream distance.
• Volumetric rate Q is constant in time.
• Incompressible liquid; no lateral inflow/outflow.

Concept / Approach:

Steady means properties at a fixed point do not change with time; constant Q satisfies that. Uniform refers to constancy along the flow direction at a given instant. Because area A(x) increases, continuity v(x) = Q / A(x) decreases with x, so velocity is not spatially constant—hence non-uniform. Therefore, the correct classification is steady non-uniform flow.

Step-by-Step Solution:

Verification / Alternative check:

A diffuser at constant throughput is the canonical steady non-uniform device; velocity and dynamic head decrease downstream while static pressure rises, consistent with Bernoulli plus losses.

Why Other Options Are Wrong:

Steady uniform: Would require constant area or special profile giving constant v; not the case.Unsteady options: Contradict the given constant rate condition.Periodic uniform: No periodic time variation is described.

Common Pitfalls:

Equating constant discharge with uniformity; it guarantees steadiness, not spatial uniformity.

Final Answer:

steady non-uniform flow