Identify the single incorrect statement about common hydraulic concepts:

Difficulty: Medium

Correct Answer: Two-dimensional flow means streamlines are necessarily straight lines; curved streamlines cannot be two-dimensional.

Explanation:


Introduction / Context:
This item checks conceptual clarity on energy composition, venturimeter geometry, Pitot tube use, and the meaning of two-dimensional flow. Only one statement is intentionally incorrect.



Given Data / Assumptions:

  • Inviscid-energy picture for Bernoulli's components (pressure, velocity head, elevation).
  • Standard venturimeter with smooth convergent and longer diffuser.
  • Pitot tube measures stagnation and static pressure for local velocity.
  • Two-dimensional flow refers to dependence on two spatial coordinates.


Concept / Approach:
Two-dimensional (2D) flow is defined by velocity components u(x,y,t), v(x,y,t) with no variation in the third coordinate. Streamlines may be curved or straight in 2D; curvature does not make the flow 3D. Venturimeters use a longer diffuser to limit adverse pressure gradients and suppress separation.



Step-by-Step Solution:

Evaluate (a): Correct — Bernoulli energy per unit weight is pressure head + velocity head + elevation head.Evaluate (b): Correct — divergent section is longer/shallower to minimize losses.Evaluate (c): Correct — Pitot tube provides local velocity via dynamic pressure.Evaluate (d): Incorrect — 2D flow can have curved streamlines; curvature does not imply 3D.


Verification / Alternative check:
Classic 2D potential flows (e.g., around a cylinder) have strongly curved streamlines yet remain 2D (no spanwise variation).



Why Other Options Are Wrong:

  • (a), (b), (c) are standard and widely taught facts.
  • (e) claims all are correct, which is false because (d) is incorrect.


Common Pitfalls:
Equating streamline curvature with three-dimensionality; assuming equal convergent and divergent lengths in a venturimeter.



Final Answer:
Two-dimensional flow means streamlines are necessarily straight lines; curved streamlines cannot be two-dimensional.


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