Mouthpieces and pressure head — absolute pressure at vena contracta In external or internal mouthpieces, when the atmospheric pressure head is equivalent to 10.3 m of water, the absolute pressure head at the vena contracta can drop to zero under sufficient driving head. Is this statement correct?
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ACorrect
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BIncorrect
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CCorrect, but only for gas flow
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DIncorrect, absolute pressure can be negative
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ECorrect only for sharp-edged orifices
Answer
Correct Answer: Correct
Explanation
Introduction / Context:In short-tube (mouthpiece) flows, the pressure at the vena contracta can fall below atmospheric. When the vacuum equals the local atmospheric head (~10.3 m of water at sea level), the absolute pressure approaches zero, which triggers a change in flow regime (e.g., mouthpiece running full) or cavitation limits.
Given Data / Assumptions:
- Water at standard conditions; atmospheric head ≈ 10.3 m of water.
- Well-formed vena contracta occurs inside the mouthpiece.
- Neglecting dissolved gases and vapor pressure nuances for the conceptual limit.
Concept / Approach:Absolute pressure head h_abs = h_atm − h_vac. If h_vac → h_atm (≈ 10.3 m), then h_abs → 0. At or below this limit, cavitation (or flow alteration) occurs; practical operation avoids approaching the absolute zero because vapor pressure is reached earlier (~0.2–0.3 m head for water at room temperature).
Step-by-Step Solution:
Recognize that p_abs ≥ 0 by definition; negative absolute pressure is nonphysical.As driving head increases, local pressure at vena contracta drops.At the limiting case where vacuum head = 10.3 m, p_abs → 0 head of water.This condition qualitatively explains transitions like mouthpiece running full.Verification / Alternative check:Engineering texts describe that when absolute pressure at the vena contracta is reduced sufficiently, separation patterns change and full running occurs; also, vapor pressure is reached prior to zero absolute in practice.
Why Other Options Are Wrong:
- “Incorrect” conflicts with the conceptual limit statement.
- Absolute pressure cannot be negative; that option is physically impossible.
- Limiting to gas flow or sharp-edged orifices is unnecessary; the concept is general.
Common Pitfalls:Equating the practical cavitation onset (at vapor pressure) with zero absolute pressure; zero is a theoretical limit, cavitation starts earlier.
Final Answer:Correct