16-Civ-B4 Engineering Hydrology · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, December 2017, 16-Civ-B4 Engineering Hydrology, three hours’ duration, closed book with one two-sided candidate-prepared aid sheet (8½″ × 11″) and one approved Casio or Sharp calculator whose model designation must be written on the first inside left-hand sheet of the work book. Seven problems are printed. Page-1 Note 4 states that any five (5) questions constitute a complete paper and that only the first five answers appearing in the work book will be marked; Note 5 weights each problem at twenty (20) points, so the examinable total is 5 × 20 = 100 points. All seven problems are solved here, because this set is a study resource rather than a timed sitting. Sub-part mark values below are the printed ones from the page-6 marking scheme, which on this sitting is internally consistent — every problem’s sub-parts sum to twenty.
Reference texts. V. T. Chow, D. R. Maidment and L. W. Mays, Applied Hydrology (hydrologic cycle, unit hydrographs, routing, frequency analysis, infiltration); L. W. Mays, Water Resources Engineering, 3rd ed. (design application, stormwater management, reservoir operation); W. Viessman and G. L. Lewis, Introduction to Hydrology, 5th ed. (measurement, areal precipitation, hydrologic modelling); C. W. Fetter, Applied Hydrogeology, 4th ed. (Darcy’s law, confined and unconfined aquifers, storativity); V. T. Chow, Open-Channel Hydraulics (1959) (flood-wave propagation and unsteady flow). Canadian practice references: Environment and Climate Change Canada / Water Survey of Canada HYDAT archive and the ECCC Engineering Climate Datasets (short-duration rainfall IDF curves and the IDF_CC climate-adjustment tool); ISO 1100-2 and the WMO Manual on Stream Gauging (stage–discharge rating practice); the Transportation Association of Canada Guide to Bridge Hydraulics and provincial highway drainage manuals (culvert design); and the Canadian Dam Association Dam Safety Guidelines (inflow design flood and flood-wave routing).
Check — the illustrative data below are the solver’s own. Every problem on the December 2017 paper is a discussion question, and the paper supplies no numerical data whatsoever. Where a short calculation appears below it exists only to demonstrate the method concretely and to make the answer checkable; its input values are stated explicitly in a Given line as assumed, representative Canadian values. They are not exam data. A candidate who assumed different but reasonable values and carried them through consistently would earn full marks, and page-1 Note 1 expressly invites the candidate to state any assumptions made.
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.
The level-pool or storage-indication method routes a flood through a water body whose surface can be taken as horizontal, so that both the storage and the outflow are single-valued functions of the water-surface elevation. It applies to reservoirs, lakes, and to detention ponds of the kind designed in Problem 7.
Step 1 — build the storage–elevation–outflow relations for the water body. Obtain the storage–elevation curve from a bathymetric survey or from contour areas integrated over depth, and the outflow–elevation curve from the hydraulics of every outlet that operates — low-level orifice, riser, service spillway, emergency spillway — summed at each elevation. These two curves are properties of the structure, established once.
Step 2 — recast continuity into the storage-indication form. Write continuity over a time step by the trapezoidal rule and collect the unknowns on one side:
$$\frac{S_2 - S_1}{\Delta t} = \frac{I_1+I_2}{2} - \frac{O_1+O_2}{2} \quad \Longrightarrow \quad \left(\frac{2S}{\Delta t}+O\right)_2 = (I_1+I_2) + \left(\frac{2S}{\Delta t}-O\right)_1$$Everything on the right is known at the start of the step. Tabulate the auxiliary function $2S/\Delta t + O$ against elevation from the Step-1 curves; this is the storage-indication curve.
Step 3 — march through the inflow hydrograph. For each step, compute the right-hand side, enter the storage-indication curve with it, read off the outflow (and hence the elevation and storage), and carry the new state forward. The result is the outflow hydrograph and, crucially for dam safety, the maximum reservoir level reached.
Given. A detention reservoir of near-constant surface area $A_s = 0.62$ km² discharging over a broad-crested weir of crest length $L = 25$ m with coefficient $C_w = 1.7$, so that $O = C_w L h^{3/2}$ and $S = A_s h$. Routing step $\Delta t = 2$ h. At the start of the step the head over the weir is $h_1 = 0.43$ m; the inflows are $I_1 = 40$ m³/s and $I_2 = 95$ m³/s.
Find. The outflow at the end of the routing step.
The inflow reached 95 m³/s while the outflow reached only 37.8 m³/s over the same step, the balance having gone into storage and raised the pool by half a metre. That attenuation is the entire purpose of the structure, and the same computation carried through the whole hydrograph gives both the peak outflow, which sizes the downstream channel, and the peak level, which sizes the freeboard and the emergency spillway.
Difference 1 — the governing equations, and therefore what the method can represent. A lumped hydrologic method (level-pool, Muskingum, Muskingum–Cunge, lag-and-route) solves continuity alone, closed by an empirical storage relation. It has one spatial element per reach and produces one number per time step: the outflow. It cannot produce a water-surface profile, cannot represent a downstream control, and cannot reproduce backwater, because the information that would generate backwater — the momentum balance and the downstream boundary condition — is simply not in the formulation. A distributed hydraulic method solves the full Saint-Venant equations, continuity and momentum, on a mesh of cross-sections or grid cells. It produces depth and velocity everywhere at every time step, and it therefore represents backwater from a downstream control, flow reversal, the effect of a bridge or a constriction, levee overtopping and breach, and the lateral spreading of water onto a floodplain.
Difference 2 — the data, effort and stability demands. A hydrologic method needs two or three calibrated parameters per reach and an inflow hydrograph; it runs in seconds, has no stability restriction beyond a mild time-step condition, and can be calibrated against a single observed inflow–outflow pair. A hydraulic method needs surveyed cross-sections or a lidar-derived terrain model at the resolution of the features that matter, roughness assigned by land cover, structure geometry for every bridge and culvert, and boundary conditions at both ends of the domain; it must satisfy a Courant condition on the time step, may require sub-metre grid resolution through an urban area, and demands hours to days of computation for a two-dimensional model. It is also far more sensitive to input error: an incorrect downstream boundary or a missing embankment in the terrain model can invalidate the whole result in a way that a lumped model, with its coarser ambitions, cannot.
Conditions favouring each. The lumped hydrologic approach is preferred when the reach is long, prismatic and free-flowing, when the flood stays within banks, when the question asked is “what discharge arrives downstream and when” rather than “how deep does the water get on which street”, when many scenarios or a long continuous simulation must be run, and when the available data are a discharge record and little else. It is the right tool for reservoir inflow forecasting, for continuous simulation to generate a flood-frequency series, and for the routing element inside a basin-scale rainfall-runoff model. The distributed hydraulic approach is required when the answer needs a water level or an extent rather than a discharge — floodplain mapping, bridge and encroachment hydraulics, levee and dam-break analysis, urban flood modelling with streets and buildings, tidal or backwater-affected reaches, and any situation with flow reversal or with storage that is not a single-valued function of the local flow. In practice the two are used together: a hydrologic model generates the design hydrograph for the basin, and a hydraulic model routes that hydrograph through the reach of interest to produce the flood map.
The situation is a rapid snowmelt-generated wave in a mountain river propagating towards a populated reach at risk of overbank flooding. The three techniques below form a natural sequence from headwater to city, each chosen for the part of the problem it handles best.
Technique 1 — a temperature-index (degree-day) snowmelt model coupled to a conceptual rainfall-runoff model, to generate the inflow hydrograph. Nothing can be routed until the wave is generated, and for a sudden melt the generation is the dominant uncertainty. A degree-day model computes melt as $M = C_m(T_a - T_b)$ over each elevation band, using the snow-water equivalent measured at snow pillows and snow courses as the available depth and the forecast air temperature as the driver. Where a rain-on-snow event is possible, the energy-budget form is preferable because rain and wind supply energy that a temperature index does not see, and rain-on-snow is precisely the mechanism behind the most damaging floods in the coastal mountains. The output is the inflow hydrograph at the head of the routed reach, and it should be run for an ensemble of temperature scenarios rather than a single forecast.
Technique 2 — Muskingum–Cunge routing through the upstream river reaches, to translate and attenuate the wave. For the long, steep, prismatic reaches between the snowfields and the city, a hydrologic method is sufficient and fast. Muskingum–Cunge is preferred over plain Muskingum here because its parameters are computed from the channel geometry, slope and roughness rather than calibrated, which matters when the reach is ungauged, and because it recomputes the wave celerity at each flow level and so captures the fact that a large wave travels faster. This step gives the arrival time and the attenuated peak at the upstream limit of the urban reach, which is the forecast that drives the warning.
Technique 3 — a one- or two-dimensional hydraulic (Saint-Venant) model of the urban reach itself, to convert discharge into depth and extent. The question is not what discharge arrives but whether it spills, and spilling is governed by water level, which depends on channel conveyance, bridge constrictions, backwater from any downstream control, and the topography of the floodplain. A HEC-RAS unsteady model in one dimension along the channel with two-dimensional flow areas over the developed floodplain, built on a lidar terrain model, converts the routed hydrograph into a time-varying map of depth and velocity, identifies the reaches where the bank is first overtopped, and quantifies the consequences of a levee breach. This is the only one of the three that can answer the flooding-potential question directly.
A useful order-of-magnitude check accompanies the second step. For a wide channel with Manning friction, the kinematic-wave celerity is $c = \tfrac{5}{3}V$, so with a mean velocity of $V = 2.4$ m/s,
$$c = \tfrac{5}{3}(2.4) = \boxed{4.0\ \text{m/s}}, \qquad t_{\text{travel}} = \frac{45\,000}{4.0} = 11\,250\ \text{s} = \boxed{3.1\ \text{h}}$$for a city 45 km downstream. Roughly three hours of warning is available — enough for evacuation and for closing floodgates, but not enough for any physical works, which is why the mitigation strategy must be in place beforehand.
Recommended engineering strategy — upstream flood storage with an operating rule, combined with floodplain conveyance restoration through the city. The most effective single measure is to intercept the wave before it reaches the developed reach, by constructing or reoperating an upstream detention or diversion facility: a dry flood-control dam on the tributary carrying the largest melt contribution, or a diversion channel to an off-stream storage area, operated under a rule curve that requires the pool to be drawn down before the freshet season. Storage attenuates the peak in exactly the manner computed in 5(i), and it acts on every event rather than on one design flood. It is preferred over raising levees through the city, because levees transfer the problem downstream, increase the consequence of failure, and encourage further development behind them. The storage should be paired with restoring conveyance and floodplain connectivity within the urban reach — removing or replacing undersized bridges, setting back existing dikes to give the river a wider corridor, and designating the remaining floodplain as park rather than building land — and with a non-structural component: a real-time snow-pillow and stream-gauge telemetry network feeding the forecast chain described above, a published warning threshold, and land-use regulation preventing new construction in the mapped floodway.
| Quantity | Symbol | Result |
|---|---|---|
| Initial outflow over the weir | O1 | 11.98 m³/s |
| Storage-indication value at the end of the step | 2S/Δt + O | 197.07 m³/s |
| Head over the weir at the end of the step | h2 | 0.925 m |
| Routed outflow at the end of the step | O2 | 37.8 m³/s (inflow 95 m³/s) |
| Kinematic-wave celerity | c | 4.0 m/s |
| Warning lead time to a city 45 km downstream | t | 3.1 h |
