Relative discharge of mouthpieces:\nThe discharge through a convergent mouthpiece is ________ the discharge through an internal (re-entrant/Borda's) mouthpiece of the same diameter and head.

Introduction / Context:
Mouthpieces are short tubes fitted to orifices. Their discharge differs with geometry because coefficients change. A re-entrant (Borda’s) mouthpiece has a much smaller coefficient of discharge than a well-designed convergent mouthpiece, so, for the same head and diameter, the convergent type delivers substantially more flow.

Given Data / Assumptions:

• Same diameter and same head of water.
• Well-formed convergent mouthpiece running full.
• Internal re-entrant mouthpiece representing Borda’s type.

Concept / Approach:
Discharge Q = C_d * A * sqrt(2 * g * H). For re-entrant mouthpiece, C_d is about 0.5. For a convergent mouthpiece, C_d commonly lies around 0.85–0.95 (depending on details). The ratio of discharges is therefore roughly 0.9/0.5 ≈ 1.8, often summarized in basic MCQs as “about twice.”

Step-by-Step Solution:

Verification / Alternative check:
Handbook tables consistently show re-entrant coefficients near 0.5 and convergent near 0.9 for water at moderate heads, supporting a near-two ratio.

Why Other Options Are Wrong:

• Equal to: Ignores large coefficient differences.
• One-half: Reverses the comparison.
• Three fourth: Too low for typical data; underestimates improvement.

Common Pitfalls:
Confusing orifice coefficients (≈0.62) with mouthpiece coefficients; comparing to a short cylindrical mouthpiece running free instead of re-entrant.

Final Answer:
double