Question 7 of 7

Problem 7 (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) Basic design approach for a stormwater dry pond — quantity control (10 marks)

A stormwater dry pond provides quantity control by temporarily storing the peak of the inflow hydrograph and releasing it slowly back to the downstream channel through a fixed, undersized outlet, so the pond's outflow peak is far lower (and delayed) relative to its inflow peak — unlike a wet pond, the basin drains completely between events and provides no permanent water-quality treatment pool. The basic design approach proceeds in stages: (1) develop the design inflow hydrograph for the contributing watershed at the target return period, typically using the Rational Method for peak flow (small catchments) or a unit-hydrograph/SCS method for the full hydrograph shape on larger catchments; (2) set the allowable release rate as the pre-development (pre-urbanization) peak discharge for the same storm, since the object of quantity control is to prevent the developed condition from increasing downstream peak flows and eroding the receiving channel; (3) size the outlet control structure (commonly a single low-flow orifice, or an orifice plus a higher emergency spillway for storms beyond the design event) to pass no more than that allowable release rate at the maximum design pool elevation; and (4) route the inflow hydrograph through the pond using the storage-indication (Puls) method, iteratively solving continuity $I(t)-O(t)=\dfrac{dS}{dt}$ together with the pond's stage-storage and stage-discharge relationships, to find the storage volume and maximum pool elevation actually required — the required live storage is essentially the area between the inflow and outflow hydrographs on a flow-vs-time plot. Because the stated objective here is reducing downstream erosion via a "reduced first-flush" release, the outlet is typically sized to draw the pool down slowly (an extended detention time of the order of 24–40 hours for the water-quality/erosion-control storm) rather than releasing at the maximum rate the flood-control storage alone would allow, since erosive channel velocities are driven by sustained moderate flows as much as by the single flood peak.

(ii) Rational Method — 25-year composite peak runoff for A1 + A2 (10 marks)

Given.

Find. The 25-year design peak runoff at the common outlet downstream of both catchments.

Approach. A2 lies downstream of A1, so the composite catchment has two possible controlling storm durations: (1) a storm just long enough for A1 alone to be fully contributing ($t=t_1=50\ \text{min}$, with A2's flow not yet arrived at the outlet), and (2) a storm long enough for the whole composite area to be contributing ($t=t_2=75\ \text{min}$, A2's own time of concentration, which governs the outlet because A2 is the more remote sub-area). The Rational Method $Q=\dfrac{C\,i\,A}{360}$ (with $Q$ in $\text{m}^3/\text{s}$, $i$ in mm/h and $A$ in ha) is evaluated for both candidate durations using a single storm intensity consistent with each duration, and the larger governs the design — using each sub-area's own (different) duration simultaneously would double-count intensity and is not physically consistent for a single design storm.

1. Read the design intensities from the 25-year IDF curve. From Fig. 6: $i(t_1=50\ \text{min}) \approx 88\text{–}90\ \text{mm/h}$; $i(t_2=75\ \text{min}) \approx 65\text{–}67\ \text{mm/h}$ (using $i_1=88.5$, $i_2=66.5\ \text{mm/h}$ below).
2. Scenario A — only A1 contributing, storm duration $t_1$. $$Q_A = \frac{C_1 A_1 i_1}{360} = \frac{0.6\times25\times88.5}{360} = \boxed{3.69\ \text{m}^3/\text{s}}$$
3. Scenario B — both A1 and A2 contributing, storm duration $t_2$. With the composite runoff coefficient $C_{comp}=\dfrac{C_1A_1+C_2A_2}{A_1+A_2}=\dfrac{0.6(25)+0.7(35)}{60}=0.658$, $$Q_B = \frac{(C_1A_1+C_2A_2)\,i_2}{360} = \frac{(15+24.5)\times66.5}{360} = \boxed{7.30\ \text{m}^3/\text{s}}$$
4. Governing design peak. $Q_B = 7.30\ \text{m}^3/\text{s} > Q_A = 3.69\ \text{m}^3/\text{s}$, so the longer, composite-area storm governs: $$Q_{25} = \boxed{7.30\ \text{m}^3/\text{s}}$$