18-Env-A2 Hydrology and Municipal Hydraulics Engineering · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2014 — 04-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 (first five answers marked); all seven are solved below for completeness. Each question ("Problem") is worth 20 marks.
Reference texts. Chow, Open-Channel Hydraulics; Linsley, Kohler & Paulhus, Hydrology for Engineers (3rd ed.); Walski et al., Advanced Water Distribution Modeling and Management; Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.).
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 three processes interact as a closed loop rather than independently. Evaporation (plus plant transpiration) removes moisture from the stream/soil surface, replenishing atmospheric humidity and, over the growing season, restoring the soil's infiltration capacity between storms. Precipitation is the loop's input event, delivering water to the ground surface at a rate (intensity) that determines how the remaining two processes divide it. Infiltration then competes directly with surface runoff for that incoming water: whatever exceeds the soil's infiltration capacity at a given instant becomes runoff, so a wetter antecedent condition (less remaining infiltration capacity, itself set by how much evapotranspiration has occurred since the last storm) shifts the partition toward more runoff for the same rainfall — the three processes are therefore coupled through the soil-moisture storage that links them.
(1) Design storm frequency. The minor system (the piped storm sewer network) is sized for frequent, moderate storms (typically 2- to 10-year return period) to convey everyday runoff underground with no nuisance surface flooding. The major system (streets, swales, floodplains and other overland flow paths) is sized—by design intent rather than pipe capacity—to safely convey rarer, larger storms (e.g. the 100-year event) that exceed the minor system's capacity, so that the excess is routed along planned overland paths instead of flooding buildings unpredictably.
(2) Physical form and cost. The minor system is a closed, engineered conduit network (expensive per unit capacity, hidden from view, requiring CCTV/maintenance access); the major system largely reuses the existing above-ground infrastructure (road crowns, curb-and-gutter profiles, designated overland flow routes) at little or no incremental construction cost, which is why major-system planning is primarily a matter of grading and floodplain management rather than pipe design.
The basic Rational Formula (SI form) is: $$Q = \frac{C\,i\,A}{360}$$ where $Q$ is the peak discharge (m³/s), $C$ is the dimensionless runoff coefficient, $i$ is the design rainfall intensity (mm/hr) at a duration equal to the time of concentration, and $A$ is the drainage area (ha).
Two key assumptions/simplifications: (1) the design rainfall intensity is uniform in space over the whole catchment and constant in time for a duration at least equal to the time of concentration $t_c$, so that peak discharge occurs precisely when the entire catchment area is simultaneously contributing runoff to the outlet; and (2) the return period of the resulting peak discharge is taken equal to the return period of the input rainfall intensity (i.e. $C$ is treated as independent of storm frequency), which is only reasonable for catchments small and fast-responding enough that hydrograph storage/attenuation effects can be neglected.
