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) Sanitary sewer diameter for a peak flow of 300 m³/s (7 marks)

Given.

Find. Required sewer diameter $D$; check whether the velocity condition is met.

Approach. For a circular pipe flowing full, $R=D/4$; substituting into Manning's equation collapses it to a single closed-form power law in $D$, solved directly, then the resulting full-flow velocity is checked against the stipulated window.

1. Collapse Manning's equation for full flow. $$Q=\frac{1}{n}AR^{2/3}S^{1/2}=\frac{1}{n}\left(\frac{\pi D^2}{4}\right)\left(\frac{D}{4}\right)^{2/3}S^{1/2}=\frac{0.3117}{n}D^{8/3}S^{1/2}$$
2. Solve for $D$. $$D=\left(\frac{Qn}{0.3117\sqrt{S}}\right)^{3/8}=\left(\frac{(300)(0.013)}{0.3117\sqrt{0.04}}\right)^{3/8}=\left(\frac{3.90}{0.06234}\right)^{3/8}=(62.56)^{3/8}=\boxed{4.72\ \text{m}}$$
3. Check the full-flow velocity. $$A=\frac{\pi D^2}{4}=17.49\ \text{m}^2\qquad V=\frac{Q}{A}=\frac{300}{17.49}=\boxed{17.15\ \text{m/s}}$$ This is far above the 7 m/s ceiling — the velocity condition is not met at the stated 4% slope.
4. Find the corrective slope. Full-pipe $V$ and $D$ are linked to $Q$ and $S$ only through Manning's equation, so meeting $V=7$ m/s at the same $Q$ forces both a larger $D$ (from continuity, $D=\sqrt{4Q/(\pi V)}$) and a flatter grade (solved from Manning's equation at that $D$ and $V$): $$D_{corr}=\sqrt{\frac{4(300)}{\pi(7)}}=7.39\ \text{m}\qquad S_{corr}=\left(\frac{Vn}{(D_{corr}/4)^{2/3}}\right)^2=\boxed{0.37\%}$$

(ii) Off-site stormwater runoff control systems for a 25-year design life (6 marks)

Two common off-site (end-of-pipe) stormwater controls are a regional dry/wet detention pond and an infiltration basin (exfiltration system), both sited downstream of the piped minor system rather than at each individual lot.

A detention pond is designed around a stage-storage-discharge relationship: an outlet control structure (orifice/weir) throttles the release rate so the peak outflow does not exceed the pre-development (or a regulated) peak for the design storm, with the required storage volume found from a routing calculation (inflow hydrograph in, routed outflow out). Over a 25-year design life the key operation issues are progressive sediment accumulation reducing the live storage volume (requiring a maintenance dredging/clean-out program, typically every 10–20 years for a wet pond forebay), embankment and outlet-structure durability (freeze-thaw, erosion, trash/debris blockage of the low-flow orifice), and the need to periodically re-verify the stage-storage curve as the drainage area urbanizes further and the design inflow hydrograph changes.

Infiltration basins instead reduce runoff volume (not just peak) by allowing water to percolate into underlying soils, so their governing design parameter is the measured soil infiltration rate (with a safety factor) sizing the basin footprint and a maximum allowable ponding/drawdown time (typically 24–72 h, to control mosquito breeding and keep the basin available for the next storm). Over a 25-year life the dominant operation issue is clogging — fines and organic material accumulating at the infiltration surface progressively reduce the design infiltration rate, so the system needs periodic surface scarification/sediment removal and pre-treatment (a sediment forebay or vegetated filter strip) upstream to protect the infiltration surface; a secondary issue is groundwater risk (infiltrating pollutants near wellhead protection areas or where the water table is shallow), which detention ponds (surface discharge only) do not share.

In short, detention trades storage volume and mechanical outlet reliability for peak-flow control, while infiltration trades soil-clogging risk and groundwater protection for actual volume reduction; a 25-year design life makes long-term sediment/clogging management the controlling maintenance issue for both.

(iii) Estimating extreme flood runoff hydrographs, AEP ≤ 0.005 (7 marks)

For dam-safety and extreme-flood risk analyses at AEP ≤ 0.005 (return periods of 200 years or longer — often extending to the Probable Maximum Flood, an effectively zero-AEP design case), standard at-site statistical frequency analysis is unreliable because it requires extrapolating a fitted distribution far beyond the length of the observed streamflow record. A robust method for this regime is the Probable Maximum Precipitation → Probable Maximum Flood (PMP→PMF) hydrograph approach: the Probable Maximum Precipitation for the watershed is estimated meteorologically (transposing and maximizing the most severe storms physically possible for the region, using moisture-maximization and storm-transposition techniques on the historical storm catalogue), then this design rainfall is routed through a calibrated rainfall-runoff/unit-hydrograph model of the watershed (accounting for antecedent soil moisture, snowmelt contribution if relevant, and channel/reservoir routing) to produce the corresponding extreme flood hydrograph.

This deterministic approach is preferred over pure statistical extrapolation at such low AEPs because it is anchored to a physically-derived upper-bound rainfall rather than to the tail behaviour of a fitted probability distribution (Log-Pearson III, GEV, etc.), whose extrapolation uncertainty grows very large beyond about twice the record length. The unit-hydrograph/rainfall-runoff model itself is calibrated and verified against the watershed's actual observed flood events before being trusted to transform the PMP into a PMF, and the resulting PMF hydrograph (peak, volume and shape) is what governs spillway and dam-safety design for AEP ≤ 0.005 events in Canadian practice (e.g., CDA Dam Safety Guidelines).