Civil Engineering PE Hydraulics and Open-Channel Flow 3

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:

Accepted Answer

66 m³/s

Answer

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:

Accepted Answer

Flow is subcritical and depth decreases toward critical depth downstream

Answer

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:

Accepted Answer

ΔE = (y₂ − y₁)³ / (4y₁y₂)

Answer

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:

Accepted Answer

0.75 m/s

Answer

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?

Accepted Answer

Hydraulic radius equals half the water depth

Answer

The most efficient trapezoidal section (half-hexagon) has hydraulic radius R = y/2, minimizing wetted perimeter for a given area.

Civil Engineering PE Practice Test