18-Env-A2 Hydrology and Municipal Hydraulics Engineering · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2017 — 04-Env-A2 Hydrology and Municipal Hydraulics Engineering (3 hours, closed book with an 8½×11 candidate aid-sheet). Instructions state any five (5) of the seven problems constitute a complete paper (100 marks); all seven are solved in full below for completeness.
Reference texts: Linsley, Kohler & Paulhus, Hydrology for Engineers; Chow, Open-Channel Hydraulics; Walski et al., Advanced Water Distribution Modeling and Management; Davis & Cornwell, Introduction to Environmental Engineering.
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 minor system is the piped/engineered conveyance sized for frequent, smaller design storms (typically 2- to 10-year return period) — catch basins, lateral and trunk storm sewers, and manholes — whose primary function is to collect nuisance and frequent-storm runoff from streets and lots quickly and unobtrusively, keeping day-to-day rainfall off roadways and private property. The major system is the surface conveyance network (road rights-of-way graded as shallow channels, overland flow routes, swales) sized to safely convey the rarer, larger design storm (often 100-year) that exceeds the minor system's piped capacity, directing the excess along predetermined, non-damaging overland paths (streets acting as open channels) to a receiving watercourse or storage facility rather than allowing uncontrolled flooding of buildings.
The two integrate as a "dual drainage" design philosophy: the minor system is deliberately sized to a moderate return period (not the full range of possible storms) because piping every conceivable storm underground is uneconomical, and the major system is explicitly designed (road crown/gutter geometry, catch-basin capacity limits, safe overland flow routes) to take over conveyance once the minor system surcharges, so that even a storm well beyond the minor system's design return period is routed safely rather than causing uncontrolled property flooding.
Cavitation occurs when the local absolute pressure within a flowing liquid (most commonly at the pump impeller eye, where velocity is highest and pressure is lowest) drops to or below the liquid's vapour pressure at the operating temperature, causing vapour bubbles to form; these bubbles are then swept into a higher-pressure region (further into the impeller or volute) where they collapse violently (implode), generating localized high-pressure shock waves that pit and erode impeller and casing surfaces, produce characteristic noise/vibration, and cause a loss of pump efficiency and head. It occurs when the Net Positive Suction Head available (NPSHA, set by suction-side elevation, pressure and friction losses) falls below the pump's required NPSH (NPSHR, a function of impeller design and speed) — common triggers are excessive suction lift, a long/undersized suction line with high friction loss, low atmospheric pressure (high altitude), or elevated liquid temperature (higher vapour pressure).
One way to eliminate or reduce cavitation: increase NPSHA — lower the pump relative to the source (reduce or eliminate suction lift, or provide a flooded suction), shorten and/or upsize the suction piping to cut friction losses, or reduce pumping temperature, so that NPSHA is kept comfortably above the manufacturer's stated NPSHR with margin.
A pump curve plots head delivered vs. flow rate for one pump. When two identical pumps operate in series (discharge of the first feeds the suction of the second), the same flow passes through both, but each adds its own head at that flow — so the combined curve is obtained by doubling the head at every flow rate, which is why, at any given flow, the series curve sits at twice the head of the single-pump curve (illustrated in the schematic as the "Two Pumps in Series" curve starting at roughly double the single pump's shut-off head and remaining at double the head across the flow range).
When two identical pumps operate in parallel (each drawing from a common suction header and discharging into a common manifold), each pump sees the same head but contributes its own flow at that head — so the combined curve is obtained by doubling the flow at every head, which is why, at any given head, the parallel curve delivers twice the flow of the single-pump curve. In both cases the actual operating point is where the combined pump curve intersects the system (head-loss) curve, not simply "double" the single-pump operating point, because system friction loss rises with flow — parallel operation in particular delivers less than double the single-pump flow once the system curve is accounted for, since the higher combined flow also raises friction losses.
