Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Biological and engineering measures to control erosion
Question Statement:
A 10 m long concrete pipe is required to carry a peak discharge of 1.0 m³ s⁻¹ in a drop inlet spillway with a head of 4 m. The entrance loss coefficient is 0.5 and the friction loss coefficient is 0.02. Consider g = 9.81 m s⁻². The neutral slope of the water level in per cent is __________ (rounded off to 2 decimal places).
Official Answer Key:
4.69 to 4.80
Step-by-Step Solution & Explanation
Method (SCS drop-inlet spillway pipe design): the pipe diameter and flow velocity are first found from the energy equation H = (1+K_e+fL/D)V²/(2g) together with continuity Q=(π/4)D²V (the “1” representing the exit velocity head, K_e the entrance loss coefficient, and fL/D the pipe friction loss). The “neutral slope” is then the slope at which the pipe's own friction slope, S_f = fV²/(2gD), equals the pipe's physical slope — i.e. the slope at which the pipe flows just full at atmospheric pressure throughout (uniform/normal flow), expressed as a percentage.
Discrepancy noted: solving the coupled equations for D and V and then evaluating S_f with the values given, our independent calculation returned values well outside the officially listed range of 4.69–4.80% under each plausible interpretation of the “friction loss coefficient” we tested (as a lumped dimensionless loss coefficient, and as a Darcy friction factor requiring the solved pipe diameter). We were not able to fully reconstruct the exact intended formula/coefficient convention from the problem statement alone. We therefore report the official key value, S_n ≈ 4.69–4.80%, as the answer, while flagging this as an item where independent re-derivation did not converge and should be cross-checked against the original SCS drop-inlet design chart/formula used in the source textbook.
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