Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow through orifices, weirs and notches
Question Statement:
In an irrigation channel, water passes through a 90° triangular weir with 36 cm head, then (with no loss) through a 1.0 m long rectangular weir further downstream. Using Francis' formula, find the head over the rectangular weir (cm).
Options:
(A) 22.1
(B) 18.4
(C) 15.0
(D) 11.8
Official Answer Key:
C
Step-by-Step Solution & Explanation
Triangular (90°) weir discharge: Q = (8/15)Cd√(2g)·tan45°·H^2.5 (Cd≈0.6) = (8/15)(0.6)(4.429)(0.36)^2.5 ≈ 0.110 m³/s. Equating to Francis' rectangular (suppressed) weir formula, Q = 1.84·L·H₂^1.5, with L=1.0 m: H₂ = (Q/1.84)^(1/1.5) ≈ 0.153 m ≈ 15.0 cm.
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