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:

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:

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