Borda’s mouthpiece running full — select the correct statement for the coefficients and velocities at the outlet.

Introduction / Context:
A Borda mouthpiece is a short tube fitted to a vessel or tank orifice. It may run free (jet separated) or run full (tube running full after the vena contracta). Understanding the discharge behavior and coefficients in these two modes is essential in fluid measurement and hydraulic design.

Given Data / Assumptions:

• Short, sharp-edged mouthpiece (Borda type).
• “Running full” means the separated jet fills the mouthpiece downstream, so the effective contraction at the outlet disappears.
• Standard definitions: coefficient of velocity Cv, contraction Cc, and discharge Cd = Cc * Cv.

Concept / Approach:

For a Borda mouthpiece running free: Cc ≈ 0.5, Cv ≈ 1, Cd ≈ 0.5. When it runs full, the effective outlet area equals the mouthpiece area, implying Cc → 1, and Cv remains close to 1, thus Cd ≈ 1 (neglecting small friction losses). Dimensional correctness also matters: velocities scale with sqrt(2 * g * H), not g * H or 2 * g * H.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Compare to orifice equation: Q = Cd * A * sqrt(2 * g * H). For running full Borda, Cd ≈ 1 → Q ≈ A * sqrt(2 * g * H), consistent with Cc = 1 and Cv ≈ 1.

Why Other Options Are Wrong:

(a) and (b) have wrong dimensions (velocity must scale with sqrt(g * H)); (c) Cv = 1/2 contradicts experimental data for sharp-edged exits; (e) is false because only one statement is correct.

Common Pitfalls (misconceptions, mistakes):

Confusing running free with running full; ignoring dimensional analysis when judging velocity formulas.

Final Answer:

Coefficient of contraction is 1