18-Env-A2 Hydrology and Municipal Hydraulics Engineering · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2013 — 04-Env-A2 / Hydrology and Municipal Hydraulics Engineering. 3 hours duration; closed book with a candidate-prepared 8½×11 in double-sided aid sheet; Casio or Sharp approved calculator only. Any five questions constitute a complete paper (first five answers marked, 20 marks each, 100 marks total); all seven are solved below for completeness.
Reference texts. Davis & Cornwell, Introduction to Environmental Engineering (6th ed.) — hydrology, stormwater management and water-demand chapters; Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.) — sanitary sewer hydraulics, Manning/Harmon design formulas; MWH’s Water Treatment: Principles and Design (3rd ed.) — distribution systems, pipe-network analysis and pump selection; Chow, Open-Channel Hydraulics — Manning's n tables and specific-energy theory; Chow, Maidment & Mays, Applied Hydrology — flood-frequency analysis; CCME water quality guidelines — cold-water fishery thermal protection.
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 hydrologic equation (a water-balance statement) partitions precipitation (or snowmelt) input $P$ over a watershed as $P=R+ET+I+\Delta S$, where $R$ is runoff, $ET$ is evapotranspiration, $I$ is infiltration and $\Delta S$ is the change in surface/depression and soil-moisture storage. The abstractions — everything on the right side except $R$ — are what prevents all precipitation from becoming runoff: interception by vegetation canopy intercepts and evaporates a portion before it even reaches the ground; depression storage fills small surface irregularities (potholes, puddles) that must be satisfied before overland flow begins; infiltration, governed by soil texture, land cover and antecedent moisture, is usually the largest single abstraction, following a Horton- or Green-Ampt-type decay curve (highest rate on dry soil, falling toward a steady saturated rate); and evapotranspiration continuously removes moisture between and during storms. For a typical watershed, only once these abstractions are satisfied (interception and depression storage full, infiltration rate exceeded by rainfall intensity) does runoff begin, which is why a short, intense storm on already-wet (low-abstraction-capacity) soil generates proportionally far more runoff than the same rainfall depth on dry soil at the start of a storm season.
(a) Sanitary forcemains. A forcemain is a pressurized sanitary pipe downstream of a lift/pumping station, used wherever gravity flow is impractical (flat terrain, a low point that must be pumped up and over a ridge, or a long transmission run to a treatment plant). Unlike a gravity sewer it flows full under pump-generated pressure, so it is sized from pump/system-curve hydraulics (not Manning's equation) and must maintain a minimum scouring velocity (typically ≥0.6–0.9 m/s) at low-flow conditions to prevent septic solids from settling and generating odour/corrosion (H₂S) problems, and requires air-release/vacuum valves at high points and thrust restraint at bends because it operates under continuous internal pressure. (b) Stormwater culvert. A culvert conveys stormwater (or a natural watercourse) under an obstruction such as a road or rail embankment; its importance lies in maintaining the pre-development drainage pattern and hydraulic capacity through the crossing so upstream ponding/flooding is not created by the embankment, and its sizing (inlet vs. outlet control, headwater depth limits) is a distinct hydraulic problem from a sewer network because it commonly operates under a wide range of flow depths (open-channel to fully submerged/pressurized) rather than steady pipe-full design flow.
Given. An urban watershed whose Rational Method time of concentration is $t_c\approx20$ min (illustrative); design return period $T=5$ yr.
Find. How the 5-year IDF curve is used to obtain the design rainfall intensity, and how it feeds the minor-system pipe sizing.
Worked example: the designer first estimates $t_c$ for the catchment (overland-flow travel time plus any existing gutter/pipe travel time upstream of the design point) — taken here as 20 minutes. Entering the IDF chart at $t=20$ min and reading up to the 5-year curve gives a design intensity of approximately $i\approx68$ mm/hr. This intensity is then substituted directly into the Rational Method, $Q=CiA/360$, together with the catchment's runoff coefficient $C$ and area $A$, to obtain the peak design flow used to size the storm sewer reach immediately downstream of that inlet. Because $t_c$ (and therefore the governing intensity) generally differs for every downstream reach as tributary area accumulates, this read-off-and-substitute step is repeated reach-by-reach moving down the pipe network, each time using that reach's own accumulated $t_c$ on the same 5-year curve. The same chart also lets the designer sanity-check a proposed pipe against a rarer event: reading the same duration off the 25-year curve instead of the 5-year curve shows how much the design intensity (and hence the required capacity) would grow, which is exactly the comparison a municipality uses when deciding whether to upsize a reach for future climate or land-use change rather than replace it again in twenty years.
