Identifying steady, uniform flow – examples Which of the following most correctly represents a steady, uniform flow situation?

Introduction / Context:
Textbook examples help cement the difference between steady/unsteady (time variation) and uniform/non-uniform (space variation). Correct classification supports valid use of Bernoulli and continuity in designs.

Given Data / Assumptions:

• “Long pipe” implies constant cross-section and adequate entrance length.
• “Rate” refers to volumetric flow rate Q.
• Fluid is incompressible and properties are time-invariant for steady cases.

Concept / Approach:

Uniform flow means velocity magnitude is the same at successive cross-sections (averaged). Steady flow means velocity at each fixed point is time-invariant. A constant Q in a constant-area conduit satisfies both.

Step-by-Step Solution:

Verification / Alternative check:

In an expanding tube at constant Q, velocity changes along the length (non-uniform), though it may be steady. Changing Q with time makes the flow unsteady regardless of geometry.

Why Other Options Are Wrong:

(a) and (e) vary with time → unsteady. (c) Steady but non-uniform. (d) Both non-uniform and unsteady.

Common Pitfalls:

Equating “steady” with “same everywhere”; assuming developing boundary layers violate uniformity—here we refer to section-averaged velocity and a sufficiently long, fully developed pipe.

Final Answer:

a long pipe at constant rate