A broad-crested weir with crest length L and head h uses Q ≈ Cd L sqrt(2 g h) with Cd ≈ 0.6. If L=3 m and h=0.5 m, approximate Q.

• A. 3.20 m^3/s
• B. 5.63 m^3/s
• C. 8.10 m^3/s
• D. 1.50 m^3/s

Answer: (B)

Discharge over a broad-crested weir scales with the crest length and the square root of the head, adjusted by a discharge coefficient: Q ≈ Cd × L × sqrt(2 g h). Here, Cd is about 0.6.

Plug in L = 3 m, h = 0.5 m, g ≈ 9.81 m/s^2:

2 g h = 2 × 9.81 × 0.5 = 9.81, so sqrt(2 g h) ≈ 3.132.

Then L × sqrt(2 g h) = 3 × 3.132 ≈ 9.396.

Finally, Q ≈ 0.6 × 9.396 ≈ 5.64 m^3/s.

The closest match is the option around 5.63 m^3/s, so that choice is the best.