Orifices and Mouthpieces MCQ with answer and solution

Concept

A convergent mouthpiece has no vena contracta and very small losses, so C_d ≈ 1.

Formula

Q = C_d × a × √(2gH), with C_d = 1 for a convergent mouthpiece

Step-by-step solution

1. Take C_d = 1 for a convergent mouthpiece. 2. Area a = (π/4) × 0.075² = 0.004418 m². 3. Velocity V = √(2 × 9.81 × 5) = √98.1 = 9.905 m/s. 4. Q = 1 × 0.004418 × 9.905 = 0.04376 m³/s. 5. Q ≈ 43.8 litres/sec.

Explanation

A convergent mouthpiece gives a smooth flow with no contraction of the jet at the outlet. So the coefficient of discharge is taken as 1. Then Q = a√(2gH) gives about 43.8 L/s.

Why the other options are wrong

A (38.2) and B (40.4) imply C_d values of about 0.87 and 0.92, which are not used for a convergent mouthpiece. D (46.1) is more than the ideal discharge, which is not possible.

Shortcut

Q = 4.43 × a × √H = 4.43 × 0.004418 × 2.236 ≈ 0.0438 m³/s.

Common mistake

Using C_d = 0.62 (orifice) or 0.855 (external cylindrical mouthpiece) instead of 1.