18-Env-A2 Hydrology and Municipal Hydraulics Engineering · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 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, $L$ | 3000 m |
| Diameter, $D$ | 300 mm = 0.300 m |
| Full-flow velocity, $V$ | 3 m/s |
| Manning's $n$ (PVC, as given) | 0.017 |
| Kinematic viscosity, $\nu$ (water) | $1.0\times10^{-6}\ \text{m}^2/\text{s}$ |
Find. (a) $Q$ in m³/min; (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, $Q$ | 12.72 m³/min |
| Reynolds number, $Re$ | 9.00×10&sup5; (turbulent) |
| Implied pipe slope | 8.22% |
| Friction head loss, $H_f$ | 246.7 m |
(1) Transmission and distribution mains (pipes). These convey and distribute treated water from the source/treatment plant to service connections. Pipe material, age and internal condition affect both quantity (increasing $C$-value degradation/tuberculation raises friction loss, reducing deliverable flow and pressure over time) and quality (internal corrosion or biofilm growth can leach metals, cause discoloration, or harbour pathogens, and leaking joints allow pathogen intrusion during low/negative-pressure events).
(2) Storage reservoirs/tanks (elevated or ground-level). These equalize the mismatch between a relatively constant treatment/pumping rate and the highly variable diurnal demand, and provide fire-flow and emergency reserve — directly affecting quantity/reliability (system can meet peak-hour and fire demand without oversizing every pipe and pump). They affect quality through water age: excessive detention time in an oversized or poorly-turned-over tank allows disinfectant residual (chlorine) to decay and can promote nitrification or biofilm growth, particularly in the tank's stagnant corners, so tank sizing and mixing/turnover are a direct water-quality decision, not just a capacity one.
(3) Pumping stations. These provide the energy to overcome elevation and friction losses and maintain system pressure. They govern quantity/reliability directly (pump capacity and standby redundancy set the system's peak deliverable flow and its resilience to a power outage), and affect quality indirectly through the pressure they maintain — a loss of positive pressure anywhere in the network (pump trip, main break) creates a risk of pathogen intrusion through leaking joints, which is why maintaining a minimum positive pressure everywhere in the distribution system at all times is a core design/operational requirement.
A widely used conceptual model for predicting peak runoff is the SCS (NRCS) Curve Number unit-hydrograph model: rainfall excess is computed from a lumped Curve Number (CN, representing the watershed's soil group, land cover and antecedent moisture condition) via the SCS runoff equation, and that excess is then convolved with a synthetic unit hydrograph (e.g., the SCS dimensionless unit hydrograph) to produce the runoff hydrograph, including its peak. It is "conceptual" because CN and the unit hydrograph time parameters are physically-motivated lumped representations of watershed response rather than a full physically-based (distributed) hydraulic solution, which makes it practical to apply where only limited observations exist.
Calibration. Model parameters (CN, time of concentration/lag time, and any routing coefficients) are adjusted so the model reproduces observed rainfall-runoff events from the watershed's own (even if short) streamflow record — typically by minimizing the error between simulated and observed peak flow and hydrograph volume/shape across several historical storms of varying size.
Verification. The calibrated model is then run, without further parameter adjustment, against an independent set of observed events not used in calibration (a split-sample test — e.g., calibrate on one set of years, verify on a different set) to confirm the model generalizes rather than having simply been fit to the calibration data; if the model reproduces the verification events' peaks and volumes within an acceptable tolerance, it is considered validated for use in design (e.g., estimating peak runoff for storms beyond the observed record, or for a future land-use scenario).
