Identify the single incorrect statement about common hydraulic concepts:
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AThe total energy of a liquid particle equals the sum of pressure energy, kinetic energy, and potential energy.
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BIn a venturimeter, the divergent (diffuser) is longer than the convergent to reduce separation losses.
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CA Pitot tube is used to measure the local flow velocity at a point in a pipe or channel.
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DTwo-dimensional flow means streamlines are necessarily straight lines; curved streamlines cannot be two-dimensional.
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EAll of the above are correct.
Answer
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.