Question 6 of 7: IDF Curves, the Rational Method, and Dry Pond Design

Problem 6: IDF Curves, the Rational Method, and Dry Pond Design (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) IDF Curve and Rational Formula — How They Work Together

The IDF curve gives the design rainfall intensity $I$ for a chosen return period as a function of storm duration $t$. The Rational Method sets the design duration $t$ equal to the catchment's time of concentration $t_c$ (the time for the entire catchment to begin contributing runoff simultaneously to the outlet, which is the duration that produces the peak flow), reads the corresponding intensity $I=I_{t_c}$ off the IDF curve at the chosen return period, and combines it with the catchment's runoff coefficient $C$ and area $A$ via $Q=CiA/360$ (SI units) to give the peak design flow.

Two assumptions. (1) The design storm has a uniform intensity across the whole catchment for the entire duration $t_c$ — an idealized, spatially and temporally uniform rainfall. (2) The peak flow occurs precisely when the entire catchment area is simultaneously contributing runoff at $t=t_c$ (a steady-state assumption, with no storage/attenuation effects along the flow path considered) — both simplifications are reasonable only for small, fast-responding catchments, which is why the Rational Method is not used for large urban trunk-sewer design (Problem 5(ii)).

(ii) Peak Flow from the Rational Method with the Given IDF Equation

Given. A 100 ha catchment with $C=0.5$, $t_c=60$ min, $I_{24}=20$ mm/hr, and the site IDF relation $\dfrac{I_t}{I_{24}}=\dfrac{1400^{0.47}}{t}$ ($t$ in minutes).

Find. Peak flow $Q$ from the catchment.

Approach. Use the given IDF equation to convert $I_{24}$ to the $t_c$-duration intensity $I_t$, then apply the Rational formula $Q=CiA/360$ (SI, $i$ in mm/hr, $A$ in ha, $Q$ in m³/s).

1. Duration-adjusted intensity. With $t=t_c=60$ min: $$I_t=I_{24}\cdot\frac{1400^{0.47}}{t}=20\times\frac{1400^{0.47}}{60}=20\times\frac{30.11}{60}=\boxed{10.0\ \text{mm/hr}}$$
2. Rational formula. $$Q=\frac{C\,I_t\,A}{360}=\frac{0.5\times10.0\times100}{360}=\boxed{1.39\ \text{m}^3/\text{s}}$$

(iii) Dry Pond — Purpose and Key Design Features

The main purpose of a dry pond is temporary detention: it stores stormwater runoff during a storm event and releases it slowly afterward through a controlled outlet, attenuating the peak flow reaching the downstream system, while remaining dry (or nearly so) between storms rather than holding a permanent pool.

Riser (with emergency spillway above it). The riser is the primary controlled outlet — a vertical structure with orifices/weirs at set elevations that meters the release rate as the pond fills, so the pond drains down over a design time rather than dumping its stored volume all at once; the emergency spillway above it is a secondary, non-erosive overflow path that safely passes flows exceeding the design storm without overtopping (and potentially breaching) the embankment.

Riprap at the outlet. Dissipates the kinetic energy of water discharging from the riser/outlet pipe before it reaches the receiving channel, preventing scour and erosion at the point of concentrated, high-velocity outflow that unprotected soil could not withstand.

Sediment forebay. A smaller, separated pre-settling cell at the pond's inlet that captures coarse sediment and debris from incoming flow before it reaches the main storage volume, protecting the pond's active storage and outlet structure (particularly the riser orifices) from progressive sedimentation and clogging, and concentrating maintenance (periodic dredging) in one accessible, small area rather than across the whole pond footprint.