18-Env-A2 Hydrology and Municipal Hydraulics Engineering · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2019 — 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. 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.); Davis & Cornwell, Introduction to Environmental Engineering (6th 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.
Given.
| Quantity | Value |
|---|---|
| Length, $L$ | 2000 m |
| Diameter, $D$ | 400 mm = 0.400 m |
| Full-flow velocity, $V$ | 4 m/s |
| Manning's $n$ (steel, as given) | 0.015 |
| Kinematic viscosity, $\nu$ (water) | $1.0\times10^{-6}\ \text{m}^2/\text{s}$ |
Find. (a) $Q$; (b) $Re$ and flow type; (c) $H_f$ in m.
Approach. $Q$ from continuity; classify with $Re$; since a Manning's $n$ is given (rather than a roughness height), back out the slope implied by Manning's equation at this $V$ and $D$, then convert to head loss over the pipe length.
| Quantity | Value |
|---|---|
| Flow rate, $Q$ | 0.5027 m³/s (30.16 m³/min) |
| Reynolds number, $Re$ | 1.60×10&sup6; (turbulent) |
| Implied pipe slope | 7.756% |
| Friction head loss, $H_f$ | 155.1 m |
(1) Conveyance and pressure maintenance (transmission/distribution mains). The pipe network's primary function is delivering treated water from the source/treatment plant to every service connection while maintaining a minimum positive pressure everywhere in the system at all times (typically ≥140–350 kPa depending on jurisdiction) — the governing design/operation constraint, since a pressure loss anywhere risks pathogen intrusion through leaking joints and cross-connections.
(2) Storage and demand equalization (reservoirs/elevated tanks). Storage facilities buffer the mismatch between a relatively constant treatment/pumping rate and highly variable diurnal demand, and provide the emergency and fire-flow reserve that would otherwise require oversizing every pipe and pump in the network; their operational aspect is water age — poor turnover in an oversized or poorly-mixed tank lets disinfectant residual decay and can promote nitrification, so tank sizing/turnover is a direct water-quality decision.
(3) Pressure boosting and zoning (pumping stations and pressure zones). Pumping stations supply the energy to overcome elevation change and friction loss across the service area; in areas with large elevation differences, the system is divided into separate pressure zones (each with its own hydraulic grade line, connected by pressure-reducing valves or booster pumps) so that no zone experiences either sub-minimum pressure (at high elevation) or excessive, main-damaging pressure (at low elevation) — a core design aspect governing both reliability and pipe-material/pressure-class selection.
A widely used conceptual model for predicting runoff is the SCS (NRCS) Curve Number method combined with a synthetic unit hydrograph: rainfall excess is computed from a lumped Curve Number (CN, representing the watershed's hydrologic soil group, land cover and antecedent moisture condition) via the SCS runoff equation, and that excess rainfall is convolved with a dimensionless synthetic unit hydrograph to produce the full runoff hydrograph, including its peak and volume. Its use is to allow reasonable design-storm runoff estimates on ungauged or sparsely-gauged watersheds, where a full physically-based distributed model cannot be calibrated for lack of data, using only readily available soil-survey and land-cover information.
Limitation 1 — lumped, non-physical parameterization. Curve Number and the unit-hydrograph time parameters are empirically-fitted lumped representations, not physically measured quantities, so the model can reproduce an observed peak flow for the "wrong" physical reason (e.g., over-estimating infiltration loss while compensating with an error in the timing parameter); this limits its reliability when extrapolated well beyond the conditions (soil groups, storm sizes, land uses) under which the original SCS curve-number tables were developed.
Limitation 2 — no explicit treatment of antecedent conditions or storm pattern. The standard SCS method assumes a single antecedent-moisture class and a fixed (Type II, etc.) design rainfall temporal pattern; it does not dynamically track soil moisture between storms or respond to a real, irregular rainfall hyetograph the way a continuous physically-based model would, so it is poorly suited to continuous simulation (e.g., a multi-storm wet season) or to watersheds whose antecedent-moisture behaviour differs materially from the standard assumption (e.g., strongly seasonal frozen-ground conditions).
