Combined sewer section, 85 ha area

Assumptions

Sewage 135 lpcd, of which 80% reaches the sewer; peak factor 3; $n=0.013$ for concrete; circular section running full at peak flow; intensity from the assumed formula $i=\dfrac{760}{t+10}$ mm/hr with storm duration 26 min.

Step 1: Discharge

$$\begin{aligned} Q_{sew}&=\frac{1500\times135\times0.8\times3}{86400\times1000}=0.0056\ \text{m}^3/\text{s}\\ i&=\frac{760}{26+10}=21.11\ \text{mm/hr}\\ Q_{storm}&=\frac{0.45\times21.11\times85}{360}=2.243\ \text{m}^3/\text{s}\\ Q&=Q_{sew}+Q_{storm}=2.249\ \text{m}^3/\text{s} \end{aligned}$$

Step 2: Slope

$$S=\frac{\text{fall}}{\text{length}}=\frac{22}{5000}=0.00440\approx\frac{1}{227}$$

Step 3: Size

$$D=\left(\frac{Q\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{2.249\times0.013}{0.3117\times0.0663}\right)^{3/8}=1.139\ \text{m}$$

Adopt $D=1.200$ m. Then $v_f=\dfrac{0.3969}{0.013}(1.200)^{2/3}S^{1/2}=2.29$ m/s and $Q_f=2.586$ m³/s.

Step 4: Check

The full-flow velocity of 2.29 m/s is greater than the required self-cleansing velocity of 0.98 m/s and below the maximum of 3 m/s, so the section is satisfactory. At the very small dry weather flow (about 0.0056 m³/s) the velocity in this big pipe will be lower, so a small low-flow channel (cunette) in the invert or an egg-shaped section is advisable.

Answer: A circular combined sewer of about 1200 mm (1.2 m) diameter at a slope of 22/5000 (1 in 227), carrying 2.249 m³/s at a velocity of 2.29 m/s.