Internal (re-entrant) mouthpiece: effect of length on jet behavior For an internal (re-entrant) mouthpiece fitted to a tank wall, which statements about jet behavior versus mouthpiece length (relative to its diameter) are correct?

Introduction / Context:
Mouthpieces are short tubes attached to orifices. An internal (re-entrant or Borda’s) mouthpiece projects into the tank. Depending on its length-to-diameter ratio, the jet may either contract and pass through without wetting the wall (running free) or expand to contact the wall (running full), changing the discharge coefficient.

Given Data / Assumptions:

• Internal (re-entrant) mouthpiece with sharp entry.
• Length-to-diameter ratio varied from about 1 to about 3.
• Steady head, incompressible flow, negligible air effects.

Concept / Approach:
Short re-entrant mouthpieces cause a vena contracta inside the tube; the core jet remains detached from the wall (running free). As length increases, boundary layers grow and the jet expands, touching the wall, so the mouthpiece runs full. Texts commonly cite transitions near L ≈ D (free) and L ≈ 3D (full).

Step-by-Step Solution:

Verification / Alternative check:
Discharge coefficients differ: running-free coefficients are lower than running-full values, matching qualitative behavior observed in experiments on Borda’s mouthpieces.

Why Other Options Are Wrong:

• Choosing only one misses the documented length effects.
• “Neither” contradicts established mouthpiece behavior.

Common Pitfalls:
Confusing internal (re-entrant) with external mouthpieces; ignoring end contractions and length-scale effects.

Final Answer:
both (a) and (b)