Civil Engineering PE Hydraulics and Open-Channel Flow 2 — Questions and Answers
Question 1: A rectangular channel 4 m wide carries water at a depth of 1.2 m with a velocity of 2.5 m/s. What is the Froude number?
- 0.63
- 0.73 (Correct answer)
- 0.83
- 0.93
Correct answer: 0.73
Fr = V/√(g·y) = 2.5/√(9.81×1.2) = 2.5/3.431 ≈ 0.73, indicating subcritical flow.
Question 2: The hydraulic radius of a trapezoidal channel with bottom width 3 m, side slopes 1.5H:1V, and depth 1.5 m is most nearly:
- 0.82 m
- 0.92 m (Correct answer)
- 1.02 m
- 1.12 m
Correct answer: 0.92 m
A = (3 + 1.5×1.5)×1.5 = 7.875 m², P = 3 + 2×1.5×√(1+1.5²) = 8.41 m, R = 7.875/8.41 ≈ 0.94 m, nearest answer 0.92 m.
Question 3: Which condition defines critical flow in an open channel?
- The energy gradient equals the channel slope
- The specific energy is at its minimum for a given discharge (Correct answer)
- The hydraulic radius equals the hydraulic depth
- The velocity equals the wave speed of a long wave in still water
Correct answer: The specific energy is at its minimum for a given discharge
Critical flow occurs when specific energy is minimized for a given discharge, which corresponds to Fr = 1.
Question 4: A 600 mm diameter circular pipe flowing half-full has a hydraulic radius of:
- 100 mm
- 150 mm (Correct answer)
- 200 mm
- 300 mm
Correct answer: 150 mm
For a half-full circular pipe, R = D/4 = 600/4 = 150 mm.
Question 5: A hydraulic jump occurs in a rectangular channel with upstream depth y₁ = 0.4 m and upstream velocity V₁ = 6 m/s. The sequent depth y₂ is most nearly:
- 1.6 m
- 1.8 m
- 2.0 m (Correct answer)
- 2.2 m
Correct answer: 2.0 m
Fr₁ = 6/√(9.81×0.4) = 3.03; y₂ = y₁(√(1+8Fr₁²)−1)/2 = 0.4×(√73.4−1)/2 ≈ 2.0 m.
Question 6: Manning's equation for open channel flow requires which parameter to account for channel roughness?
- Darcy friction factor f
- Manning's roughness coefficient n (Correct answer)
- Chezy's coefficient C
- Reynolds number Re
Correct answer: Manning's roughness coefficient n
Manning's equation Q = (1/n)A·R^(2/3)·S^(1/2) uses n as the dimensionless roughness coefficient.
Question 7: The critical depth in a rectangular channel 5 m wide carrying a discharge of 20 m³/s is most nearly:
- 0.94 m
- 1.37 m (Correct answer)
- 1.74 m
- 2.17 m
Correct answer: 1.37 m
yc = (q²/g)^(1/3) where q = 20/5 = 4 m²/s; yc = (16/9.81)^(1/3) = (1.631)^(1/3) ≈ 1.37 m.
Civil Engineering PE Hydraulics and Open-Channel Flow 2
A rectangular channel 4 m wide carries water at a depth of 1.2 m with a velocity of 2.5 m/s.
What is the Froude number?