18-Env-A2 Hydrology and Municipal Hydraulics Engineering · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 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 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.
Precipitation is the input to the system; its form, intensity and duration set the volume and rate of water available to become runoff. In a rural (vegetated) watershed, canopy interception captures a portion of the rainfall before it ever reaches the ground, delaying the onset of runoff and reducing the effective rainfall depth compared to an equivalent storm over bare or paved ground.
Infiltration is the process that most strongly distinguishes a rural watershed's hydrologic response from an urban one: permeable, vegetated soils typically have a high infiltration capacity, so a large share of the precipitation that reaches the ground is diverted to soil moisture and groundwater recharge rather than to the surface. This produces a smaller-peak, more attenuated, delayed runoff hydrograph than the same storm would produce over impervious urban surfaces.
Evapotranspiration (evaporation from soil/surface water plus plant transpiration) returns a substantial fraction of the water balance to the atmosphere, especially during the growing season in a vegetated rural catchment. By removing water from the soil-moisture store between storms, evapotranspiration replenishes the soil's infiltration/storage capacity, which further increases the runoff-reducing effect of infiltration in subsequent storms and moderates the long-term (seasonal) water yield of the stream.
A drop structure is a hydraulic structure built into a storm sewer or open drainage channel where the invert elevation falls abruptly (a vertical or stepped drop) at a discrete location, rather than allowing the pipe or channel to follow a continuously steep natural ground slope. Its primary function is to control the effective hydraulic grade/bed slope of the system — concentrating the elevation change and the associated energy dissipation at one designed location — so that pipe or channel velocities elsewhere remain within non-erosive limits.
Two important design considerations: (1) energy dissipation — the structure must include an adequately sized stilling basin, baffle blocks or plunge pool (commonly designed around a hydraulic jump) to dissipate the kinetic energy of the falling water and prevent scour or undermining at the structure's downstream toe; and (2) hydraulic and structural capacity — the structure must convey the design flow without excessive backwater (afflux) upstream of the drop, and must be structurally robust against the impact and uplift forces of the falling jet, with (for sanitary/combined applications) attention to turbulence-induced odour and corrosion (H₂S) generation at the drop.
| Term | Significance | Dimensions (SI) |
|---|---|---|
| $Q$ | Discharge (pipe/channel flow rate) being conveyed | m³/s |
| $n$ | Manning's roughness coefficient — empirical measure of the pipe/channel surface's resistance to flow | dimensionless |
| $A$ | Cross-sectional area of flow | m² |
| $R$ | Hydraulic radius, $R=A/P$ (flow area divided by wetted perimeter) | m |
| $S$ | Slope of the energy grade line (≈ pipe/bed slope for uniform flow) | dimensionless (m/m) |
Manning's Equation is the standard uniform-flow relation used to size storm sewers: for a selected pipe material (fixing $n$) and an available bed slope $S$, the designer solves for the pipe diameter (through $A$ and $R$, both functions of diameter and depth of flow) that conveys the design discharge $Q$ without surcharging. Because $R^{2/3}S^{1/2}$ appears explicitly, the same discharge can be conveyed by a smaller pipe on a steeper slope or a larger pipe on a flatter slope — the trade-off municipal designers use to fit a sewer network to the available ground slope while respecting minimum (self-cleansing) and maximum (non-erosive) velocity limits.
