Orifices & mouthpieces – Relative coefficient of discharge Compared to a short external (projecting) mouthpiece, the coefficient of discharge Cd for a short internal (re-entrant, Borda’s) mouthpiece is generally:
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Aless than
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Bmore than
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Cequal to
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Dunrelated to
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Egreater at high heads but smaller at low heads
Answer
Correct Answer: less than
Explanation
Introduction:Mouthpieces modify the flow leaving an orifice. Their geometry affects contraction, velocity distribution, and thus the discharge coefficient Cd. A common comparison is between a short internal (re-entrant) mouthpiece, often called Borda's mouthpiece, and a short external projecting mouthpiece.
Given Data / Assumptions:
- Sharp-edged openings; steady flow from a large reservoir.
- Short internal re-entrant mouthpiece vs short external mouthpiece.
- Neglect significant viscous losses beyond those embedded in Cd.
Concept / Approach:
In a re-entrant (internal) mouthpiece, the jet contracts more severely at the vena contracta located approximately at the mouthpiece plane, producing a smaller effective area and lower Cd (around 0.5). In contrast, short external mouthpieces that run full typically have Cd nearer 0.82–0.85. Hence, Cd(internal) < Cd(external).
Step-by-Step Solution:
Step 1: Identify stronger contraction in the re-entrant geometry.Step 2: Recall typical Cd values: internal ≈ 0.5; external short ≈ 0.82.Step 3: Conclude “less than.”Verification / Alternative check:
Classic hydraulics experiments (Borda) document reduced discharge for re-entrant openings compared to plain or externally projecting mouthpieces at the same head.
Why Other Options Are Wrong:
More than / equal / unrelated: Inconsistent with observed contraction behavior and standard data.Head-dependent reversal: While Cd varies slightly with head, the ordering does not invert in the usual operating range.
Common Pitfalls:
Confusing coefficients of contraction, velocity, and discharge. Remember Cd = Cc * Cv and strong contraction lowers Cc and thus Cd.
Final Answer:
less than