Civil Engineering PE Hydraulics and Open-Channel Flow 4 — Questions and Answers
Question 1: A circular culvert D = 900 mm flows full with L = 30 m, n = 0.013, and S = 0.005. Normal discharge using Manning's equation is most nearly:
- 1.8 m³/s
- 2.4 m³/s (Correct answer)
- 3.0 m³/s
- 3.6 m³/s
Correct answer: 2.4 m³/s
A = π(0.9)²/4 = 0.636 m², R = 0.225 m; Q = (1/0.013)(0.636)(0.225^0.667)(0.005^0.5) ≈ 2.4 m³/s.
Question 2: The momentum function (M) in open channel flow is most useful for analyzing:
- Gradually varied flow profiles
- Hydraulic jumps and rapidly varied flow (Correct answer)
- Normal depth in prismatic channels
- Flow measurement over sharp-crested weirs
Correct answer: Hydraulic jumps and rapidly varied flow
The momentum function M = Q²/(gA) + ȳA is conserved across a hydraulic jump, making it ideal for rapidly varied flow analysis.
Question 3: In the direct step method for GVF profile computation, the channel reach length Δx between two depth sections is computed as:
- Δx = ΔE / (S₀ − S̄f) (Correct answer)
- Δx = ΔE × (S₀ + S̄f)
- Δx = Δy / (S₀ − S̄f)
- Δx = ΔV / (S₀ − S̄f)
Correct answer: Δx = ΔE / (S₀ − S̄f)
The direct step method solves Δx = ΔE/(S₀ − S̄f), where ΔE is the specific energy change between two chosen depths.
Question 4: A 90° V-notch (triangular) weir with Cd = 0.60 measures a head H = 0.4 m. The discharge is most nearly:
- 0.056 m³/s
- 0.071 m³/s (Correct answer)
- 0.090 m³/s
- 0.113 m³/s
Correct answer: 0.071 m³/s
Q = (8/15)Cd√(2g)·tan(45°)·H^(5/2) = (8/15)(0.60)(4.429)(1)(0.4^2.5) = 1.416×0.1012 ≈ 0.071 m³/s.
Question 5: Normal depth in an open channel is the depth at which:
- The Froude number equals 1.0
- Specific energy is minimized
- The gravitational driving force equals the friction resistance (uniform flow) (Correct answer)
- The channel slope changes from mild to steep
Correct answer: The gravitational driving force equals the friction resistance (uniform flow)
Normal depth occurs during uniform flow when the gravitational force exactly balances friction resistance, resulting in constant depth and velocity.
Question 6: A broad-crested weir has crest elevation 100 m, upstream water surface at 101.8 m, width L = 5 m, and Cd = 0.848. Discharge is most nearly:
- 10.4 m³/s
- 14.6 m³/s (Correct answer)
- 20.8 m³/s
- 29.2 m³/s
Correct answer: 14.6 m³/s
H = 1.8 m; Q = 1.705·Cd·L·H^(3/2) = 1.705×0.848×5×(1.8)^1.5 ≈ 14.6 m³/s.
Question 7: When a subcritical flow channel width narrows sufficiently, 'choking' occurs at the constriction. This means:
- Flow velocity drops to zero at the throat
- Critical depth is forced at the throat, limiting the discharge (Correct answer)
- A hydraulic jump forms immediately upstream
- The flow becomes supercritical throughout the channel
Correct answer: Critical depth is forced at the throat, limiting the discharge
Choking forces critical depth at the throat when the available specific energy equals the minimum required; the upstream depth must rise to supply additional energy.
Civil Engineering PE Hydraulics and Open-Channel Flow 4
A circular culvert D = 900 mm flows full with L = 30 m, n = 0.013, and S = 0.005.
Normal discharge using Manning's equation is most nearly: