Design discharge from given data

The design discharge of a combined sewer is the peak sanitary sewage plus the storm water runoff.

Assumptions

• Permeability 60% means the area is 40% impervious, so $C=1-0.60=0.40$.
• Rainfall intensity for the given storm duration of 15 min is taken from $i=\dfrac{760}{t+10}$ mm/hr (assumed empirical formula, $t$ in min).
• Time of concentration $t_c=t_e+t_f=5+15=20$ min (the storm of 15 min is used for intensity as given).

Step 1: Sanitary sewage

Average sewage = 80% of 100 lpcd = 80 lpcd. Peak = 3 x average.

$$Q_{sewage}=\frac{75000\times100\times0.8\times3}{86400\times1000}=0.2083\ \text{m}^3/\text{s}$$

Step 2: Storm water

Area $A=8\ \text{km}^2=800$ ha.

$$\begin{aligned} i&=\frac{760}{15+10}=30.40\ \text{mm/hr}\\ Q_{storm}&=\frac{C\,i\,A}{360}=\frac{0.40\times30.40\times800}{360}=27.022\ \text{m}^3/\text{s} \end{aligned}$$

Step 3: Design discharge

$$Q=Q_{sewage}+Q_{storm}=0.2083+27.022=27.231\ \text{m}^3/\text{s}$$

Answer: Design discharge = 27.231 m³/s (storm water 27.022 m³/s plus sewage 0.2083 m³/s). If the examination supplies its own intensity formula, replace $i$ and the same steps apply.