Question 4 of 7: Sanitary Sewer Design, Stormwater Runoff Control, and Flood-Risk Probability Curves

Problem 4: Sanitary Sewer Design, Stormwater Runoff Control, and Flood-Risk Probability Curves (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 — Full-Flow Manning Design

Given. A corrugated steel sanitary sewer must convey a peak flow of 5 m³/s flowing full.

Find. Required full-flow diameter $d$ (nearest mm) and confirmation the velocity limits are met.

Approach. Solve Manning's full-pipe equation $Q=\dfrac{1}{n}\left(\dfrac{\pi d^2}{4}\right)\left(\dfrac{d}{4}\right)^{2/3}S^{1/2}$ for $d$ (numerically, since $d$ appears to a non-integer power), round to the nearest mm, then recompute $V=Q_d/A$ at that diameter and check it against the 0.8–8 m/s bound.

1. Set up the full-flow Manning equation. With $A=\pi d^2/4$ and full-pipe hydraulic radius $R=d/4$: $$Q_d=\frac{1}{n}\cdot\frac{\pi d^2}{4}\cdot\left(\frac{d}{4}\right)^{2/3}\cdot S^{1/2}$$
2. Solve for $d$ numerically (bisection on $d$ so that the right-hand side equals $Q_d=5.0\ \text{m}^3/\text{s}$ with $n=0.025$, $S=0.05$): $$d=\boxed{1245\ \text{mm}}\ (\text{nearest mm, rounded from }1244.9\ \text{mm})$$
3. Check the velocity limits. $A=\pi(1.245)^2/4=1.218\ \text{m}^2$: $$V=\frac{Q_d}{A}=\frac{5.0}{1.218}=\boxed{4.11\ \text{m/s}}$$ Since $0.8\ \text{m/s}<4.11\ \text{m/s}<8\ \text{m/s}$, both velocity conditions are satisfied at the required diameter.

(ii) On-Site and Off-Site Stormwater Runoff Control

On-site: permeable pavement / infiltration trench at a parking lot or roadway (source control installed on the contributing lot itself). Its important design feature is an open-graded stone reservoir course beneath the permeable surface that temporarily stores runoff and allows it to infiltrate into the native subgrade, directly reducing both the peak and the total volume of runoff leaving the site before it ever reaches the public storm sewer; periodic vacuum-sweeping of the surface is required to keep the infiltration voids from clogging with fines.

Off-site: regional wet detention pond receiving flow from multiple upstream developments via the trunk storm sewer (a downstream, shared facility rather than a lot-level device). Its important design feature is an outlet structure (orifice and/or weir) sized to attenuate the routed peak inflow to a target post-development discharge rate, with a permanent pool providing additional water-quality treatment through settling — giving both quantity control (flood-peak attenuation for everything tributary to it) and a measure of quality control at a single downstream location.

(iii) Reservoir Elevation Probability Curve — Derivation and Use in Dam Routing

Derivation. An annual-maximum series of inflow (or resulting reservoir elevation) is assembled from the gauge/hydrologic record for the watershed and fitted to a flood-frequency distribution (e.g. Log-Pearson Type III or Gumbel EV1); the fitted distribution gives the median (expected) elevation at each annual exceedance probability (AEP), while the 95% confidence limits are obtained from the sampling variance of the fitted parameters (or a Monte-Carlo resampling of the historical record), producing the solid median curve and dashed uncertainty band plotted against AEP.

Use in dam-overflow routing. The curve supplies the design inflow/elevation at a chosen AEP (the design flood standard for the structure) together with its uncertainty band; reservoir routing — balancing the inflow hydrograph against the outlet-controlled outflow through the spillway and/or gates, $I(t)-O(t)=dS/dt$ — is then performed at that design elevation, using the upper (95%) confidence bound for a conservative freeboard and spillway-capacity check. This confirms the dam crest and spillway can pass the routed outflow without overtopping, and by attenuating the peak through temporary reservoir storage during the routing, limits the incremental downstream flood peak during less-frequent, higher-magnitude events.