Classifying pipe flow at constant rate along a long, prismatic pipe A flow through a long pipe at a constant volumetric rate is best described as:

Introduction / Context:
Flow classification depends on time variation (steady vs. unsteady) and spatial variation along the streamline (uniform vs. non-uniform). Understanding these terms helps interpret measurements and apply the correct governing equations and loss models.

Given Data / Assumptions:

• Constant volumetric flow rate Q (no time variation).
• Long, prismatic pipe of constant diameter and roughness.
• Single-phase incompressible liquid; temperature changes negligible.

Concept / Approach:
Steady means properties at a fixed point do not change with time (∂()/∂t = 0). Uniform means properties do not change along the direction of flow at a given instant. In a constant-diameter pipe with constant Q, the average velocity V = Q/A is constant along the pipe; though pressure drops due to friction, velocity magnitude remains spatially uniform.

Step-by-Step Solution:

Verification / Alternative check:
Bernoulli with head loss explains pressure drop along the pipe without change in average speed for a constant area, consistent with “uniform.”

Why Other Options Are Wrong:

• Steady non-uniform: would require area change (nozzle/diffuser) or imposed acceleration.
• Unsteady options: contradict constant-rate condition.

Common Pitfalls:
Confusing uniformity of velocity with uniformity of pressure. Uniform flow does not imply constant pressure; it implies constant velocity magnitude along the streamline for constant area.

Final Answer:
Steady uniform flow