Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
A rectangular channel having bed slope of 0.05% and Manning’s roughness coefficient of 0.01 carries a discharge of 5 m³ s⁻¹. If the channel is designed as the most economical section, the width of the channel in meter will be __________.
Official Answer Key:
2.45 to 2.50
Step-by-Step Solution & Explanation
• Most economical (hydraulically efficient) rectangular section: b = 2y, giving hydraulic radius R = y/2.
• Manning’s equation: Q = (1/n) A R^(2/3) S^0.5, with A = by = 2y².
• Q = (1/0.01)(2y²)(y/2)^(2/3)(0.0005)^0.5.
• (0.0005)^0.5 = 0.02236. (y/2)^(2/3) = y^(2/3)/1.5874.
• 5 = 100 × 2y² × y^(2/3)/1.5874 × 0.02236 = 2.8175 y^(8/3).
• y^(8/3) = 5/2.8175 = 1.7748 ⇒ y = 1.7748^(3/8) ≈ 1.240 m.
• b = 2y ≈ 2.48 m, inside the accepted range 2.45–2.50.
Section 6 — Agricultural Process Engineering
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