External Mouthpiece — Parameter Affecting Coefficient of Discharge For an external (projecting) mouthpiece attached to a tank orifice, which geometric or flow parameter most significantly influences the coefficient of discharge Cd?

Introduction:
Mouthpieces are short tubes fitted to orifices that alter jet contraction and energy losses. The discharge coefficient Cd depends on how the jet forms and attaches within the mouthpiece, which is strongly affected by its length and shape.

Given Data / Assumptions:

• External (projecting) mouthpiece, sharp entry from the tank.
• Steady discharge under a given head.
• Negligible air entrainment and cavitation.

Concept / Approach:
For very short lengths, the jet exhibits a vena contracta with significant contraction losses; as length increases moderately, the jet expands to fill the tube (“running full”), reducing contraction losses and changing Cd. Thus, the mouthpiece length relative to diameter governs the regime and resulting discharge coefficient.

Step-by-Step Solution:
Classify regimes: running free vs running full.Increase length beyond about 2–3 diameters to promote running full.Observe Cd changes accordingly; therefore, length is the key influence.

Verification / Alternative check:
Laboratory measurements show Cd for external mouthpieces increases as the mouthpiece length permits the jet to adhere and fill the passage.

Why Other Options Are Wrong:
Velocity and pressure are consequences of head; area changes capacity but does not by itself determine loss mechanisms the way length does.

Common Pitfalls:
Ignoring entrance shape and edge sharpness; confusing with nozzles where contouring dominates.

Final Answer:
length of mouthpiece