Civil Engineering PE Hydraulics and Open-Channel Flow 5 — Questions and Answers
Question 1: The Chezy coefficient C is related to Manning's n by which expression (SI units)?
- C = n·R^(1/6)
- C = R^(1/6) / n (Correct answer)
- C = n / R^(1/6)
- C = √R / n
Correct answer: C = R^(1/6) / n
Equating Manning's V = (1/n)R^(2/3)S^(1/2) and Chezy's V = C√(RS) gives C = R^(1/6)/n.
Question 2: Flow in a steep channel (S₀ > Sc) with depth greater than critical depth carries which GVF profile classification?
- S1 (Correct answer)
- S2
- S3
- M1
Correct answer: S1
An S1 profile occurs on steep slopes when y > yc; depth decreases downstream toward normal depth, with flow remaining supercritical.
Question 3: A rectangular channel 3 m wide carries Q = 15 m³/s at normal depth with n = 0.014 and S₀ = 0.001. Normal depth is most nearly:
- 1.45 m
- 1.75 m (Correct answer)
- 2.05 m
- 2.35 m
Correct answer: 1.75 m
Using Manning's iteratively: Q = (1/0.014)(3y)[(3y/(3+2y))^(2/3)](0.001^0.5) = 15 m³/s yields yn ≈ 1.75 m.
Question 4: For a sluice gate in a wide rectangular channel with upstream depth y₁ = 2.0 m, gate opening a = 0.3 m, and Cc = 0.62, discharge per unit width assuming negligible velocity of approach is most nearly:
- 0.74 m²/s
- 1.17 m²/s (Correct answer)
- 1.47 m²/s
- 1.85 m²/s
Correct answer: 1.17 m²/s
q = Cc·a·√(2g·y₁) = 0.62×0.3×√(2×9.81×2.0) = 0.186×6.264 ≈ 1.17 m²/s.
Question 5: The primary purpose of a stilling basin downstream of a spillway is to:
- Increase tailwater depth to raise reservoir levels
- Dissipate kinetic energy via a controlled hydraulic jump to prevent scour (Correct answer)
- Create supercritical conditions for accurate flow measurement
- Reduce sediment transport rates through sedimentation
Correct answer: Dissipate kinetic energy via a controlled hydraulic jump to prevent scour
A stilling basin forces a hydraulic jump, converting high-velocity supercritical flow to subcritical and dissipating kinetic energy to protect the downstream channel.
Question 6: The standard step method for GVF computation differs from the direct step method primarily because the standard step:
- Only applies to prismatic channels while the direct step applies to non-prismatic channels
- Specifies depth increments and directly solves for distance
- Specifies distance increments and iterates to find the corresponding depth (Correct answer)
- Uses the momentum equation while the direct step uses the energy equation
Correct answer: Specifies distance increments and iterates to find the corresponding depth
The standard step method fixes the distance increment and iterates to find depth at each section; it applies to non-prismatic channels where cross-section geometry varies.
Question 7: A circular conduit flowing at approximately 0.94D depth (not full) carries what fraction of its full-flow discharge?
- About 90% of full-flow discharge
- About 100% of full-flow discharge
- About 108% of full-flow discharge (Correct answer)
- About 115% of full-flow discharge
Correct answer: About 108% of full-flow discharge
Due to circular pipe geometry, maximum discharge occurs near 0.94D depth and is approximately 108% of the full-pipe discharge.
Civil Engineering PE Hydraulics and Open-Channel Flow 5
The Chezy coefficient C is related to Manning's n by which expression (SI units)?