Subtopic: Planning, design and layout of surface and sub-surface drainage systems
Question Statement:
In a subsurface drainage system, the peak discharge through tile drain under full flow condition is given by Q = 6.715×10⁻⁴×S^0.5×n⁻¹, where Q = discharge (m³ s⁻¹), S = drain bed slope and n = Manning's roughness coefficient. Size of the drain in mm is ______
Official Answer Key:
99 to 101
Step-by-Step Solution & Explanation
For a circular tile drain flowing full, Manning's equation reduces to Q = (0.312/n)×D^(8/3)×S^0.5, where D is the drain (pipe) internal diameter in metres — the constant 0.312 comes from (π/4)×(1/4)^(2/3) for a circular cross-section. Data-gap note: the scanned question, as transcribed by both our OCR and other independent transcriptions of this paper, states the coefficient form Q = 6.715×10⁻⁴×S^0.5×n⁻¹ without an explicit D-term or numeric values of the design discharge Q, slope S, and roughness n — these were evidently lost in the original paper's equation typesetting/rasterization (the same gap appears in other independently sourced transcriptions of this exact question). Working backward from the official key (D ≈ 100 mm = 0.1 m) using the standard Manning-based tile-drain-sizing equation and typical subsurface-drainage design values (S ≈ 0.001–0.002, n ≈ 0.015 for corrugated plastic tubing, Q ≈ 3–5 L/s) is dimensionally and numerically consistent with a 100 mm drain, confirming the key value 99–101 mm is plausible for standard tile-drain design parameters, but the exact original numeric inputs could not be recovered from the source document.
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