16-Civ-A5 Hydraulic Engineering · May 2013

Question 5 of 6: River blockage by a slope failure

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper: National Exams — 98-Civ-A5 Hydraulic Engineering, May 2013 · 3 hours, closed book (one aid sheet). Six questions; any five constitute a complete paper — all six are solved here as a study resource. All parts of a question are of equal value.

Reference texts. Mays, Water Resources Engineering, 3rd ed. (pipe systems, pumps, network analysis); Chow, Open-Channel Hydraulics (Manning flow, compound sections); Crowe, Elger & Roberson, Engineering Fluid Mechanics (energy/continuity). Exam-supplied relations used throughout: Hazen–Williams $Q=0.278\,C\,D^{2.63}\,S^{0.54}$ with $S=h_f/L$ (SI), Manning $Q=\tfrac{1}{n}A\,R^{2/3}\,S^{1/2}$, and total dynamic head $\text{TDH}=H_s+H_f$. Unless stated, local losses and velocity head are neglected, and water has $\rho=1000\ \text{kg/m}^3$.

Check (Q4 data consistency): the pipe/valve data in Question 4 are internally inconsistent — the stated “initial valve flow = 400 L/s” corresponds to a node head of only 9.5 m, but the two supply pipes driven by the 96 m and 89 m tank levels deliver far more than that at 9.5 m. Continuity at the node fixes a network-consistent initial discharge of ≈693 L/s at a node head of ≈28.4 m. The simulation below is run from that physically consistent state, with the discrepancy noted (per Note 1, candidates may state assumptions).

Question 5: River blockage by a slope failure (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — hydraulic conditions at the blockage. The instantaneous, complete blockage of a flowing river is a classic unsteady open-channel problem best read through the three conservation principles.

Continuity. Before failure the river carries a discharge $Q=VA$ that is (approximately) constant along its length. The blockage abruptly sets the through-flow at the barrier to zero. Upstream, water continues to arrive but can no longer pass, so mass accumulates: the cross-sectional storage grows and the water surface rises with time ($\partial A/\partial t = -\partial Q/\partial x > 0$). Downstream, no new water is supplied past the barrier, so the reach drains at its former discharge and the flow depth falls. Continuity therefore predicts rising storage (and stage) upstream and depleting flow downstream.

Momentum. Upstream, the arriving flow is decelerated from velocity $V$ to rest against the debris dam. That loss of momentum is delivered to the barrier as a hydrodynamic thrust in addition to the hydrostatic pressure of the ponding water; a positive surge (a moving hydraulic bore) propagates upstream at celerity $c\approx\sqrt{gA/B}$ relative to the water, carrying the “stop” signal into the approaching flow. The momentum equation across this surge relates the depth and velocity on either side (a moving-hydraulic-jump / bore balance). Downstream, the sudden cut-off launches a negative (rarefaction) wave that lowers the depth and can strand the bed; there is no sustaining momentum flux, so the downstream reach relaxes toward a trickle fed only by local inflow, seepage through the debris, and baseflow.

Energy. Upstream the kinetic energy of the moving river is converted, first into the turbulence and heat of the impact/surge (a highly dissipative, non-conservative process — energy is not conserved across the bore), then into potential energy as the pond deepens: the specific energy upstream climbs as velocity head is traded for a growing stage. The blockage itself acts like a suddenly raised broad weir/dam; once the pond overtops or seeps, flow across the debris will be steep and supercritical on the downstream face, dissipating energy in a plunge/hydraulic jump at the toe. Downstream of the barrier the flow, deprived of supply, loses energy as depth and velocity both decay.

Part (b) — impacts on the upstream storm-sewer outfall and town. The outfall sits immediately upstream, exactly where water is ponding and the stage is rising. Several specific, connected consequences follow:

Submergence and backwater at the outfall. The rising pond raises the tailwater on the storm sewer. Once the river stage exceeds the outfall invert, the outfall becomes submerged (drowned), sharply reducing its discharge capacity: the sewer must now push flow against a positive downstream head instead of a free outfall.
Surcharging and backflow into the storm system. As the pond continues to rise it can exceed the hydraulic grade line inside the storm sewer, driving river water back up the pipe. Without a flap/backflow gate, this surcharges the network, causes street and basement flooding through catch basins and low manholes, and can back river sediment and debris into the pipes.
Urban flooding from lost drainage. During any concurrent rain the town’s storm runoff can no longer discharge to the river, so the storm system backs up and surface flooding spreads — the blockage effectively removes the town’s drainage receptor.
Dam-break / overtopping hazard. The debris dam is uncompacted and unengineered. When the pond overtops or the dam fails, a sudden dam-break flood wave is released downstream — the most dangerous outcome, threatening anything (including downstream parts of the town or the exposed streambed) below the barrier.
Water-quality and public-health effects. Ponded, near-stagnant water mixing with storm-sewer discharge (and any illicit sanitary cross-connections) promotes low dissolved oxygen, odour, and contamination; the impounded reach behaves like an unplanned, poorly mixed detention pond.

Immediate engineering responses: install or verify a backflow preventer on the outfall, monitor the pond stage, and controlled-breach or notch the debris dam to lower the pond safely rather than allowing an uncontrolled overtopping failure.

Topic. Unsteady open-channel response to a sudden barrier (surges/bores) and drainage-system interaction.

Key relations. Continuity $\partial A/\partial t+\partial Q/\partial x=0$; surge celerity $c=\sqrt{gA/B}$; moving-jump momentum balance; specific energy $E=y+V^2/2g$ (energy dissipated across a bore/jump); submerged-outfall/backwater control.

Why this works. Continuity gives the direction of storage change (fill upstream, drain downstream); momentum gives the surge that carries the disturbance and the thrust on the dam; energy identifies where dissipation occurs (impact, jump) and why it is non-conservative. The drainage impacts follow directly from the rising upstream stage acting as tailwater on the outfall.

Common pitfall. Treating the event as steady, or assuming energy is conserved across the surge/impact. Bores and jumps are momentum-conserving but energy-dissipating — using Bernoulli across them is wrong.

Source. Chow, Open-Channel Hydraulics, Ch. 18–19 (unsteady flow, surges); Mays, Water Resources Engineering, Ch. 15 (stormwater/urban drainage).

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