Question 1 of 7

Problem 1 (20 marks)

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.

(i) Snow melt vs. rainfall precipitation in hydraulic design (6 marks)

Rainfall-based design can rely directly on an IDF curve because the storm's intensity and duration are the whole story: rain reaches the ground as liquid at a rate the atmosphere sets. Snow melt is different — the water is stored on the ground as a solid and released later, controlled by an energy balance rather than a storm hyetograph — so two additional engineering methods are needed:

1. Degree-day (temperature-index) melt modelling. Because melt is driven by net energy input (shortwave/longwave radiation, air temperature, wind, condensation), designers estimate melt rate as $M = C_m (T_a - T_b)$, where $C_m$ is a melt-rate (degree-day) factor calibrated to the basin and $T_b$ is a base temperature (commonly $0\,{}^{\circ}\text{C}$). This replaces the rainfall intensity term in the design hydrograph with an energy-budget-derived melt rate.
2. Snowpack storage/routing and rain-on-snow combination. A snowpack retains a water-equivalent (SWE) that can be released gradually over days to weeks (a long, low, broad hydrograph) rather than the minutes-to-hours response to rainfall, and it can also be primed by a rain-on-snow event that releases stored SWE rapidly. Hydraulic structures in snow country are therefore checked against both a rainfall design storm and a snowmelt/rain-on-snow scenario (often the annual maximum flood is a spring freshet, not a summer storm), using SWE surveys and basin storage routing rather than an IDF curve alone.

(ii) Wastewater collection system components (6 marks)

(a) Sewage pumping station. Gravity sewers must maintain self-cleansing slope, which drives pipe inverts progressively deeper with distance from the ridge line of a service area; where topography is flat or a sewer would otherwise have to be excavated uneconomically deep (or cross a summit), a pumping station lifts wastewater from a wet well back up to a shallower gravity main or directly to the treatment plant. A typical station provides screening/grinding ahead of the pumps, duplex or triplex pump sets sized so the system meets peak flow with one unit out of service (standby capacity), and level/alarm telemetry, because unlike a water main a sewage pumping station cannot simply be shut down — wastewater generation is continuous and an overflow is an environmental and public-health event.

(b) Daily per capita sewage flow. This is the design unit-flow parameter (L/capita·day) representing average domestic wastewater generation, built up from water-use records or standard allowances and adjusted for the service area's institutional/commercial contribution. Multiplying by the design population gives the average dry-weather flow; applying a peaking factor (e.g., Harmon or Babbitt formula, which decreases with population as the sewer serves more people and flows average out) gives the peak design flow used to size sewer diameters, pump station capacity and treatment-plant hydraulic loading. Infiltration and inflow (I/I) allowances are added separately, since I/I is not a function of population but of pipe condition and rainfall.

(iii) Using the IDF curves to size a trunk storm sewer (8 marks)

Approach. The Rational Method ($Q = \dfrac{C\,i\,A}{360}$, with $Q$ in $\text{m}^3/\text{s}$, $i$ in $\text{mm/hr}$ and $A$ in hectares) is the standard tool for sizing a trunk sewer serving a small, highly impervious catchment such as a large parking lot: the IDF curve supplies the design intensity once a storm duration equal to the time of concentration $t_c$ is chosen, and the resulting $Q$ is then checked against the trunk pipe's Manning capacity.

Given (illustrative). Parking lot area $A = 4\ \text{ha}$; paved surface, runoff coefficient $C = 0.95$; time of concentration $t_c \approx 20\ \text{min}$ (short inlet + gutter travel time typical of a compact paved lot); 10-year return period.

1. Read the design intensity from the 10-year IDF curve at $t = t_c$. At a duration of 20 minutes the 10-year curve gives $i_{10} \approx 100\ \text{mm/hr}$ (Fig. 1).
2. Apply the Rational Method. $$Q = \frac{C\,i\,A}{360} = \frac{0.95 \times 100 \times 4}{360} = \boxed{1.06\ \text{m}^3/\text{s}}$$ This is the peak design flow the trunk sewer downstream of the lot must convey for the 10-year storm.
3. Size the trunk sewer. With the design $Q$ fixed, the engineer selects a commercial pipe diameter and slope so that Manning's equation, $Q = \tfrac{1}{n}AR^{2/3}S^{1/2}$, delivers at least $1.06\ \text{m}^3/\text{s}$ flowing at a self-cleansing velocity (typically $\geq 0.75\text{–}0.9\ \text{m/s}$ at design flow) without surcharge, and confirms the crown of the pipe clears any adjacent utilities and meets minimum cover.