Flow classification – Long pipe with decreasing discharge over time A liquid flows through a long pipe of constant diameter, and the flow rate decreases with time while the spatial distribution along the pipe at any instant is uniform. This situation is best described as what kind of flow?

Introduction:
Flow fields are commonly classified using two axes: time variation (steady vs unsteady) and spatial variation at a given instant (uniform vs non-uniform). Correct classification is a foundational skill for interpreting continuity, momentum, and energy equations in different scenarios.

Given Data / Assumptions:

• Long pipe of constant cross-sectional area.
• At any instant, the mean velocity is the same at all axial positions (uniform in space).
• Discharge changes with time (decreasing), so velocity at a point varies with time.

Concept / Approach:

Uniform vs non-uniform refers to spatial dependence at a fixed time; steady vs unsteady refers to time dependence at a fixed point. With constant area and no leakage, continuity implies the same volumetric flow through any cross-section at a given instant, i.e., spatially uniform. However, because the discharge varies with time, the flow is unsteady. Therefore the correct label is unsteady uniform flow.

Step-by-Step Solution:

Verification / Alternative check:

Contrast with a diffuser at constant Q (steady non-uniform) or a start-up ramp in a nozzle (unsteady non-uniform). The present case matches neither, reinforcing the chosen classification.

Why Other Options Are Wrong:

Steady uniform: Violates the observed time variation.Steady non-uniform: Time-invariant but spatially varying; not our case.Unsteady non-uniform: Would require spatial variation as well; absent here.Periodic uniform: Would imply repeating temporal pattern; not stated.

Common Pitfalls:

Assuming “long” pipe implies non-uniform; length alone does not determine classification—spatial and temporal dependences do.

Final Answer:

unsteady uniform flow