Weirs and Notches MCQ with answer and solution

Concept

Discharge over a rectangular notch is Q = (2/3) C_d L √(2g) H^3/2.

Formula

Q = (2/3) × C_d × L × √(2g) × H^3/2

Step-by-step solution

1. Data: L = 1 m, H = 100 mm = 0.1 m, C_d = 0.60, √(2g) = 4.43. 2. H^3/2 = 0.1^1.5 = 0.03162. 3. Q = (2/3) × 0.60 × 1 × 4.43 × 0.03162. 4. (2/3) × 0.60 = 0.4, and 0.4 × 4.43 = 1.772. 5. Q = 1.772 × 0.03162 = 0.0560 m³/s. 6. Q = 0.0560 × 1000 = about 56.0 litres/sec. The nearest option is 56.8 litres/sec (C).

Explanation

For a rectangular notch, discharge depends on H^3/2. Putting in the values gives about 0.056 m³/s, which is 56 litres per second. The closest option is C.

Why the other options are wrong

A: 52.8 L/s is too low and does not match the formula. B: 48.5 L/s is too low. It may come from a wrong value of H^3/2. D: 62 L/s is too high. It may come from using C_d or √(2g) wrongly.

Shortcut

(2/3) × 0.6 = 0.4, so Q = 0.4 × 4.43 × L × H^1.5.

Common mistake

Using H in mm instead of m, or using H² or H instead of H^3/2.