Water Resources and Hydraulics
Water resources and hydraulics questions test continuity, energy and momentum in pipes, channels and pumps, with Egyptian applications in irrigation networks, Nile-fed systems, drainage and water supply. The exam expects correct use of Manning's equation, Froude number, pump curves and water-hammer awareness.
Core rules and concepts
- Continuity and energy: Q = AV; Bernoulli's equation with head loss is the basis of pipe and channel analysis. Separate friction losses from minor losses and apply them at the correct locations.
- Open-channel flow: Manning's equation V = (1/n)R^(2/3)S^(1/2), where R = A/P. Normal depth occurs when friction slope equals bed slope; critical depth occurs at minimum specific energy and Fr = 1.
- Froude number: Fr = V/√(gD), with D = A/T for a non-rectangular channel. Fr < 1 is subcritical, Fr = 1 critical and Fr > 1 supercritical.
- Pumps: the operating point is the intersection of the pump curve and system curve. Check NPSH available against NPSH required to avoid cavitation.
- Transients: rapid valve closure can produce water hammer; surge protection, air vessels or slow closure may be required.
Worked example
A rectangular channel is 5.0 m wide, carries water at 1.5 m depth, has bed slope 0.001 and Manning n = 0.015. A = 5 × 1.5 = 7.5 m², P = 5 + 2(1.5) = 8.0 m, R = 0.9375 m. Then V = (1/0.015)(0.9375)^(2/3)(0.001)^(1/2) = 66.67 × 0.958 × 0.0316 = 2.02 m/s. Q = AV = 15.1 m³/s. The hydraulic depth is D = A/T = 7.5/5 = 1.5 m, so Fr = 2.02/√(9.81 × 1.5) = 0.53, indicating subcritical flow.
Traps that cost marks
- Using diameter instead of hydraulic radius in Manning's equation.
- Mixing slope as a percentage with slope as a decimal.
- Treating a channel as critical because it is steep, without calculating Fr.
- Selecting a pump from its shut-off head rather than the system operating point.
- Ignoring minor losses in short, fittings-heavy pipework.
- Forgetting that water hammer pressure depends on closure time relative to the pipe period.