Name of a projecting (re-entrant) mouthpiece The mouthpiece shown projects into the tank (i.e., the opening is internally projecting or re-entrant). By which of the following names is this commonly known in fluid mechanics?

Introduction / Context:
Mouthpieces are short tubes fitted to orifices to control jet formation and discharge coefficients. When the mouthpiece projects into the tank rather than outside it, the flow separates at the sharp internal edge, creating a characteristic vena contracta. This configuration has multiple synonymous names in the literature.

Given Data / Assumptions:

• Mouthpiece is shown projecting inward (re-entrant) into the reservoir wall.
• Short length relative to diameter; sharp-edged entrance.
• Incompressible flow, moderate heads.

Concept / Approach:
An inward projecting mouthpiece is commonly called an internal mouthpiece, a re-entrant mouthpiece, or Borda’s mouthpiece (after Jean-Charles de Borda). The discharge characteristics, including coefficient of discharge and contraction, are distinct from external (projecting outward) mouthpieces because of the way the jet contracts inside the mouthpiece.

Step-by-Step Solution:

Verification / Alternative check:
Standard fluid mechanics texts list these synonyms; experimental discharge coefficients for Borda’s mouthpiece match those for re-entrant/internal forms.

Why Other Options Are Wrong:

• Each of options a–c individually names the same device; restricting to one would be incomplete given the question’s phrasing.
• “External mouthpiece” is the opposite orientation (projects outward) and therefore incorrect.

Common Pitfalls:
Confusing internal and external configurations; assuming different names imply different hardware when they are synonymous in this context.

Final Answer:
All of the above