Internal mouthpieces – condition for running free vs running full An internal mouthpiece is said to be running free if the length of the mouthpiece is __________ the diameter of the orifice:

Introduction:Flow through internal (Borda's) mouthpieces can occur in two regimes: running free (jet springs clear of the walls after vena contracta) or running full (the mouthpiece runs full like a short pipe). The regime depends largely on the mouthpiece length-to-diameter ratio.

Given Data / Assumptions:

• Sharp-edged entrance forming a vena contracta.
• Mouthpiece aligned with the orifice axis.
• Steady incompressible flow; minor losses present.

Concept / Approach:When the length is relatively short, the contracted jet does not expand enough to contact the walls; the flow is said to run free, exhibiting coefficients characteristic of orifice discharge. As the length increases beyond a few diameters, wall attachment occurs and the passage runs full, behaving closer to short-pipe flow with different coefficients.

Step-by-Step Solution:1) Define L/D as the length-to-diameter ratio.2) Empirical criterion: running free for L/D less than about 3; running full when L/D exceeds about 3.3) Therefore the correct comparative phrase is “less than three times.”

Verification / Alternative check:Observed discharge coefficients shift as L/D crosses ~3, confirming regime transition in laboratory studies.

Why Other Options Are Wrong:

• Less than twice: too restrictive; many designs run free up to near 3D.
• More than twice / more than three times / exactly four times: these tend toward running full, not free.

Common Pitfalls:Ignoring entrance shape; a rounded entrance alters contraction and regime boundaries.

Final Answer:less than three times