Short-tube mouthpiece behavior — a short tube mouthpiece will NOT run full at its outlet under which head condition?

Introduction / Context:
A short-tube (Borda-type) mouthpiece may discharge with a separated jet that does not fill the tube (“running free”) or with the tube running completely full. Whether it runs full depends on the available head and the ability of ambient pressure to sustain the separated core.

• Sharp-edged short tube attached to a tank/orifice.
• Atmospheric pressure at the outlet; negligible losses aside from separation.
• Head measured above the centerline of the mouthpiece.

Concept / Approach:

For heads below a critical value (~12.2 m of water), the separated jet persists without reattaching, and the mouthpiece does not run full. For heads exceeding this, pressure recovery can cause the jet to fill the tube (“running full”). Thus, “will not run full” corresponds to heads less than about 12.2 m of water.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Empirical data for Borda mouthpieces report Cc ≈ 0.5 (free) and Cc ≈ 1 (full) with the transition near 12.2 m head.

Why Other Options Are Wrong:

“More than” reverses the condition; “equal” is a threshold case not aligned with the “will not” phrasing; “none” and “1 m” do not reflect the known criterion.

Common Pitfalls (misconceptions, mistakes):

Confusing Borda mouthpiece behavior with long pipes; ignoring the role of separation and reattachment.

Final Answer:

less than 12.2 m of the water