18-Env-A2 Hydrology and Municipal Hydraulics Engineering · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2018 — 18-Env-A2 / Hydrology and Municipal Hydraulics Engineering. 3 hours duration; closed book with an 8.5×11 in double-sided aid sheet; Casio or Sharp approved calculator only. Any five questions constitute a complete paper (only the first five answers in the work book are marked); all seven Problems are solved below for completeness. Each question is worth 20 marks.
Reference texts. Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Linsley, Kohler & Paulhus, Hydrology for Engineers (3rd ed.); Chow, Open-Channel Hydraulics; Walski et al., Advanced Water Distribution Modeling and Management; Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.); Guidelines for Canadian Drinking Water Quality (Health Canada); Canadian Council of Ministers of the Environment (CCME) water-quality guidelines.
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.
Four key processes of the natural hydrologic cycle: evaporation (from oceans, lakes and soil into the atmosphere), condensation (water vapour forming clouds), precipitation (rain/snow reaching the land surface), and infiltration/runoff partitioning (precipitation splitting between surface runoff, soil storage, and groundwater recharge, with transpiration returning part of the stored water to the atmosphere).
Three important relationships among these processes that affect runoff from a large watershed: (1) infiltration capacity vs. rainfall intensity — runoff is generated only once rainfall intensity exceeds the soil's current infiltration capacity (Hortonian excess), so soil type, land cover and antecedent moisture directly control how much of a storm becomes runoff rather than recharge; (2) evapotranspiration and antecedent soil moisture — ET between storms dries the soil profile and restores infiltration/storage capacity, so a long dry spell before a storm reduces runoff while a wet antecedent condition (as after a preceding storm) increases it for an otherwise identical rainfall; and (3) travel time through the drainage network — the time water takes to move from where it becomes runoff to the watershed outlet (governed by slope, channel/pipe network density, and watershed size) controls how the many small local peaks combine into (or spread out from) a single watershed-outlet flood peak, which is why a large watershed's peak runoff is not simply the sum of instantaneous local runoff rates.
Given.
| Area | Area (ha) | Runoff coeff. $C$ | Time of concentration $t_c$ (min) |
|---|---|---|---|
| A1 | 25 | 0.6 | 50 |
| A2 | 35 | 0.7 | 120 |
50-year IDF curve (from the exam's IDF chart, read at each area's own $t_c$, which conveniently coincides with the chart's own duration gridlines): $i_{50}(t_c{=}50\ \text{min})\approx17.7\ \text{mm/h}$; $i_{50}(t_c{=}120\ \text{min}=2\ \text{h})\approx12.4\ \text{mm/h}$.
Find. $Q_{A1}$ and $Q_{A2}$, each in m³/min.
Approach. Rational Formula $Q=CiA/360$ (SI: $A$ in ha, $i$ in mm/h, $Q$ in m³/s), evaluated independently for each catchment using its own $C$, $t_c$ (hence its own chart intensity) and area — the two areas are given as separate catchments, not a single composite watershed in series.
| Catchment | 50-yr intensity used | Peak runoff |
|---|---|---|
| A1 (25 ha, $t_c=50$ min) | 17.7 mm/h | 44.25 m³/min |
| A2 (35 ha, $t_c=120$ min) | 12.4 mm/h | 50.63 m³/min |
The Rational Method estimates a single peak runoff rate as $Q=CiA/360$: the runoff coefficient $C$ accounts for the fraction of rainfall that becomes runoff, $i$ is the design-storm rainfall intensity evaluated at a duration equal to the catchment's time of concentration $t_c$ (the storm duration that produces the highest peak, since the whole catchment is then contributing simultaneously), and $A$ is the contributing area.
Two important assumptions: (1) the design storm's intensity is uniform over the entire catchment and constant for the whole duration $t_c$ — real storms vary in both space and time, so this assumption becomes progressively less realistic as catchment area grows; and (2) the peak runoff occurs when the ENTIRE catchment is contributing simultaneously, i.e. at a storm duration exactly equal to $t_c$ — a shorter, more intense storm does not have time to engage the whole catchment, and a longer storm has a lower average intensity, so $t_c$ is assumed to be the critical (worst-case) duration.
Implications for major stormwater conveyance system design. Because assumption (1) degrades with catchment size, the Rational Method is only applied to the individual, relatively small sub-catchments that feed the major system (streets, swales, overland flow paths), not to the major system's large, composite drainage area as a single lumped calculation — the major system's design flow is built up by routing/combining the smaller sub-catchment peaks (checking, as in part (ii), which combination of sub-areas and durations actually governs) rather than applying $C$, $i$, $A$ once to the whole watershed. And because assumption (2) ties the design intensity to each sub-catchment's own $t_c$, a major system whose overland flow paths are engineered to be shorter/faster (steeper swales, higher-capacity street cross-section) will have a SHORTER $t_c$ and therefore see a HIGHER design intensity per unit area than an otherwise identical, poorly-conveyed overland path — so major-system geometry itself feeds back into the very peak flow the major system must be sized to carry.
