Question 3 of 6: Stormwater Models and Storm Sewer Design

Problem 3: Stormwater Models and Storm Sewer 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.

(a) Stormwater Models Used in Ontario

(b) Storm Sewer Design — Areas A1 and A2

Given. Two sub-catchments in series, both draining to a common storm sewer alignment (A1 → MH1 → MH2, A2 joining at MH2 → outlet):

Find. The required pipe diameter for Pipe 1 (A1 → MH2) and Pipe 2 (MH2 → outlet, carrying A1+A2), sized so the 5-year design flow is conveyed without surcharging onto the street.

Approach. Get the design rainfall intensity from the IDF equation at $T_c$, compute each pipe's peak flow by the metric Rational Method (Pipe 2 uses the cumulative tributary area), then size each pipe from Manning's equation for full-pipe flow and round up to the next standard commercial diameter.

1. Design rainfall intensity. From the crib-sheet IDF equation $I=\dfrac{A}{(T_c+B)^c}$:$$I=\frac{1330.31}{(12+7.938)^{0.855}}=\frac{1330.31}{12.92}=\boxed{102.97\ \text{mm/h}}.$$
2. Peak flow, Pipe 1 (drains $A_1$ only). Metric Rational Method $Q=\dfrac{CIA}{360}$ ($Q$ in m³/s, $I$ in mm/h, $A$ in ha):$$Q_1=\frac{(0.45)(102.97)(0.70)}{360}=\boxed{0.0901\ \text{m}^3/\text{s}}.$$
3. Peak flow, Pipe 2 (drains cumulative $A_1+A_2=1.20$ ha).$$Q_2=\frac{(0.45)(102.97)(1.20)}{360}=\boxed{0.1545\ \text{m}^3/\text{s}}.$$
4. Size Pipe 1. Solving Manning's equation for a pipe flowing full, $Q=\dfrac{1}{n}\left(\dfrac{D}{4}\right)^{2/3}S^{1/2}\dfrac{\pi D^2}{4}$, for $D$ at $Q_1=0.0901$ m³/s gives $D_{req}=257$ mm; rounding up to the next commercial size, $D_1=\boxed{300\ \text{mm}}$. At full flow this pipe carries $Q_{full}=0.137$ m³/s ($>Q_1$, OK) at $V_{full}=1.93$ m/s.
5. Size Pipe 2. The same closed-form solve at $Q_2=0.1545$ m³/s gives $D_{req}=314$ mm; rounding up, $D_2=\boxed{375\ \text{mm}}$. At full flow this pipe carries $Q_{full}=0.248$ m³/s ($>Q_2$, OK) at $V_{full}=2.25$ m/s.
6. Check against flooding. Both commercial diameters carry more than the computed 5-year peak flow while flowing full, and both full-flow velocities (1.93 and 2.25 m/s) sit inside the conventional 0.6–3.0 m/s self-cleansing/non-scouring range for a sanitary/storm sewer — so the 5-year event is conveyed without surcharging onto the street.