Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Earthen dams
Question Statement:
An earthen embankment with a pipe spillway is constructed to create temporary storage in a gully. The pipe of 10 m length has to carry a peak discharge of 1 m³ s⁻¹ at an available head of 4 m. Entrance loss coefficient for the square entrance is 0.50 and the friction loss coefficient is 0.15. Required diameter of the pipe in m is
Options:
(A) 0.50
(B) 0.60
(C) 0.75
(D) 1.00
Official Answer Key:
B
Step-by-Step Solution & Explanation
Energy balance for a pipe flowing full under head H: H = (1 + Ke + f·L/D)·V²/2g, where the '1' accounts for the exit/velocity head, Ke=0.50 is the entrance loss coefficient, and f=0.15 is the friction loss coefficient; Q = A·V = (π/4)D²V. Solving iteratively for D with Q=1 m³/s, L=10 m, H=4 m gives D ≈ 0.544 m. Since pipe spillways are always specified to the next larger standard commercial diameter for adequate capacity margin, the design (selected) diameter rounds up to D = 0.60 m, matching option (B). (Verification note: the raw iterative solution of ≈0.544 m falls between options (A) 0.50 and (B) 0.60; standard design practice of rounding up to the next commercial pipe size resolves this to option (B).)
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