Question 6 of 7

Problem 6 (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) Stormwater dry pond design for erosion control and flood prevention (10 marks)

A stormwater dry pond (extended-detention basin, normally empty between storms) is designed around a stage-storage-discharge relationship: an outlet control structure — typically a multi-stage riser combining a small low-flow orifice with a higher-capacity overflow weir — throttles the release rate so that the routed peak outflow for each targeted design storm does not exceed a specified target, with the required storage volume found from reservoir routing (the design inflow hydrograph in, the routed outflow hydrograph out, storage = the difference integrated over time).

For the stated objectives, the pond is typically designed with (at minimum) two control stages: an extended-detention (erosion-control) stage, sized to release the frequent, smaller storms (commonly the 1-year, or a "channel-forming" event) slowly — over 24–48 hours — through a small low-flow orifice, so that the post-development peak AND duration of erosive velocities in the receiving channel does not exceed the pre-development condition (matching only the peak, without also extending the duration near bank-full flow, still causes progressive channel erosion); and a flood-control stage, sized via a higher weir to attenuate the rarer, larger design storm (often the 100-year event, matching the low-lying residential development's flood-protection target) down to at or below the pre-development peak discharge for that storm.

Key design elements are: an emergency spillway sized to safely pass the extreme (e.g., 1:100-year-plus or PMF-derived) flow without overtopping the embankment, protecting the downstream residential development from a catastrophic dam-breach-style failure; sufficient freeboard between the maximum routed water surface and the top of the embankment; and a low-flow/forebay channel through the pond bottom to prevent nuisance ponding and mosquito breeding between storms, since a dry pond (unlike a wet pond) is not meant to hold a permanent pool. Because the pond is normally dry, sediment deposited during each storm must be periodically removed from the low-flow channel and forebay to keep the outlet structure's low-flow orifice from being buried or blocked, which would otherwise silently defeat the erosion-control stage's extended-detention function.

(ii) Rational Method design peak runoff for two catchments in series (10 marks)

Given.

100-year IDF curve (read from the supplied chart, Tr = 100 years, by tracing the topmost curve at high resolution and cross-checking against a fitted $i=a/(t+b)^c$ power curve through several clean off-gridline chart points): $i\approx104$ mm/h at duration 50 min; $i\approx75$ mm/h at duration 80 min (chart-derived, ±10% engineering tolerance).

Find. The governing 100-year design peak runoff at the outlet, using the Rational Formula $Q=CiA/360$ ($Q$ in m³/s, $i$ in mm/h, $A$ in ha).

Approach. With two sub-catchments in series, the design storm duration that maximizes the OUTLET peak is not obvious a priori: a short, intense storm (duration = A1's own $t_c$) only lets A1 contribute at full intensity (A2 has not yet reached its own outlet-response time), while a longer storm (duration = A2's $t_c$, the time for the combined system to fully respond) lets the FULL combined area contribute, but at a lower intensity. Both candidate peaks are computed and the larger governs.

1. Candidate 1 — storm duration = $t_1=50$ min (only A1 fully contributing).$$Q_1=\frac{C_1A_1i(t_1)}{360}=\frac{(0.5)(40)(104)}{360}=\boxed{5.78\ \text{m}^3/\text{s}}$$
2. Candidate 2 — storm duration = $t_2=80$ min (combined A1+A2 area contributing).$$Q_2=\frac{(C_1A_1+C_2A_2)\,i(t_2)}{360}=\frac{[(0.5)(40)+(0.6)(60)]\,(75)}{360}=\frac{(56)(75)}{360}=\boxed{11.67\ \text{m}^3/\text{s}}$$
3. Governing peak. Since $Q_2=11.67\ \text{m}^3/\text{s} > Q_1=5.78\ \text{m}^3/\text{s}$, the longer storm duration (letting the full composite area contribute) governs, even though its intensity is lower:$$\boxed{Q_{100}=11.67\ \text{m}^3/\text{s}}$$