Internal Mouthpiece – Relative Discharge When Running Full vs Running Free For an internal mouthpiece, when the mouthpiece runs full (jet expands to fill it), the discharge is approximately twice the discharge obtained when it is running free (detached jet with vena contracta).

Introduction:
Short-tube orifices (mouthpieces) can operate in two regimes: running free and running full. The discharge coefficient changes markedly between these regimes, altering the flow rate for the same head.

Given Data / Assumptions:

• Internal (Borda) mouthpiece on a large reservoir.
• Same head over the mouthpiece for both operating conditions.
• Negligible cavitation and proper aeration conditions.

Concept / Approach:

When running free, the jet forms a vena contracta inside the short tube and remains detached, yielding a relatively low discharge coefficient. When the jet expands to touch and fill the tube (running full), losses associated with contraction are reduced and the effective coefficient increases significantly, giving a higher discharge for the same head. Classical data show the full-running discharge is about double that of the free-running condition.

Step-by-Step Solution:

Verification / Alternative check:

Standard orifice/mouthpiece tables report Cd_free near one-half of the full-running value for internal mouthpieces, supporting the “approximately twice” rule of thumb.

Why Other Options Are Wrong:

“Incorrect” contradicts experimental observations; additional qualifiers (small heads, submerged outlet) are not required for the fundamental comparison, though extreme conditions may slightly alter coefficients.

Common Pitfalls:

Confusing internal and external mouthpieces; overlooking air entrainment and submergence effects that can modify Cd but not the qualitative trend.

Final Answer:

Correct