All else equal for a broad-crested weir, if crest length L doubles with head h constant, how does discharge Q change?

• A. 4
• B. 2
• C. 1
• D. 0.5

Answer: (B)

For a broad-crested weir, how much water passes per unit time depends on the cross-sectional flow area across the crest and the velocity set by the head. The discharge scales with crest length times a function of head, and with head held constant, the velocity term stays the same while the flow area grows in direct proportion to the crest length. Therefore the discharge is proportional to L when h is fixed. If the crest length doubles, the discharge doubles.