Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
A concrete-lined non-circular tunnel has a semi-circle at the top and a rectangular section at the bottom. The semi-circle has a diameter of 6 m whereas the rectangular section is 6 m wide and 3 m high. The tunnel carries a discharge of 128 m³ s⁻¹. If the friction factor f = 0.017, then the head loss in 1 km length of the tunnel in m will be
Options:
(A) 0.57
(B) 1.15
(C) 2.29
(D) 4.58
Official Answer Key:
C
Step-by-Step Solution & Explanation
Flow area A = (semicircle, R=3) + (rectangle, 6×3) = (π×3²/2) + 18 = 14.14 + 18 = 32.14 m². Wetted perimeter (flowing full, so it is treated as a closed conduit — perimeter includes the curved top and the two vertical + bottom sides, but not the internal chord between semicircle and rectangle): P = π×3 + 2×3 + 6 = 9.42 + 6 + 6 = 21.42 m. Hydraulic radius R_h = A/P = 32.14/21.42 = 1.5 m; hydraulic diameter D_h = 4R_h = 6.0 m. Velocity V = Q/A = 128/32.14 = 3.98 m/s. Darcy-Weisbach head loss: h_f = f(L/D_h)(V²/2g) = 0.017×(1000/6.0)×(3.98²/19.62) = 0.017×166.7×0.807 = 2.29 m, matching option (C).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.