Civil Engineering PE Hydraulics and Open-Channel Flow 3 — Questions and Answers
Question 1: A spillway has discharge coefficient Cd = 0.85, head H = 1.5 m, and length L = 10 m. The discharge over the spillway is most nearly:
- 66 m³/s (Correct answer)
- 83 m³/s
- 99 m³/s
- 116 m³/s
Correct answer: 66 m³/s
Q = Cd(2/3)√(2g)·L·H^(3/2) = 0.85×(2/3)×4.429×10×1.837 ≈ 66 m³/s.
Question 2: In gradually varied flow (GVF), an M2 profile occurs when:
- Flow is supercritical and depth increases downstream
- Flow is subcritical and depth decreases toward critical depth downstream (Correct answer)
- Flow is subcritical and depth increases toward normal depth downstream
- Flow is supercritical and depth decreases toward normal depth upstream
Correct answer: Flow is subcritical and depth decreases toward critical depth downstream
M2 is a mild-slope profile where subcritical flow depth decreases downstream toward critical depth, occurring upstream of a free overfall.
Question 3: The energy loss in a hydraulic jump in a rectangular channel is given by:
- ΔE = (y₂ − y₁)³ / (4y₁y₂) (Correct answer)
- ΔE = (y₂ − y₁)²
- ΔE = (y₂ − y₁)³ / (2y₁y₂)
- ΔE = V₁²/(2g) − V₂²/(2g)
Correct answer: ΔE = (y₂ − y₁)³ / (4y₁y₂)
Energy loss in a hydraulic jump: ΔE = (y₂ − y₁)³ / (4y₁y₂), derived from energy and momentum equations.
Question 4: A pipe transitions from 300 mm diameter to 600 mm diameter. If velocity in the smaller pipe is 3 m/s, the velocity in the larger pipe is:
- 0.25 m/s
- 0.75 m/s (Correct answer)
- 1.50 m/s
- 6.00 m/s
Correct answer: 0.75 m/s
By continuity A₁V₁ = A₂V₂; V₂ = (D₁/D₂)²×V₁ = (0.3/0.6)²×3 = 0.25×3 = 0.75 m/s.
Question 5: For a trapezoidal channel, the most hydraulically efficient section has which property?
- Bottom width equals water depth
- Hydraulic radius equals half the water depth (Correct answer)
- Side slopes are vertical (z = 0)
- Top width equals twice the bottom width
Correct answer: Hydraulic radius equals half the water depth
The most efficient trapezoidal section (half-hexagon) has hydraulic radius R = y/2, minimizing wetted perimeter for a given area.
Question 6: A suppressed rectangular weir (no end contractions) has L = 3 m, H = 0.5 m, and Cd = 0.61. Discharge is most nearly:
- 0.96 m³/s
- 1.22 m³/s
- 1.55 m³/s
- 1.91 m³/s (Correct answer)
Correct answer: 1.91 m³/s
Q = (2/3)(0.61)(√19.62)(3)(0.5^1.5) = (2/3)(0.61)(4.429)(3)(0.354) ≈ 1.91 m³/s.
Question 7: Specific energy in an open channel is measured relative to the:
- Datum at mean sea level
- Channel invert (bottom) (Correct answer)
- Water surface elevation
- Energy grade line
Correct answer: Channel invert (bottom)
Specific energy E = y + V²/(2g) is measured relative to the channel bottom (invert), combining depth and velocity head.
Civil Engineering PE Hydraulics and Open-Channel Flow 3
A spillway has discharge coefficient Cd = 0.85, head H = 1.5 m, and length L = 10 m.
The discharge over the spillway is most nearly: