Circular sedimentation tank, population 80000

Assumptions: sewage reaching the plant $=0.78\times135 = 105.3$ lpcd, designed for the maximum rate ($2.5\times$ average): $Q_{avg}=80000\times 105.3/1000 = 8424.0$ m³/day. Detention 2 h and depth 3 m are adopted; two tanks are provided. Silica $d=0.12$ mm ($G=2.65$) at 20°C.

Step 1: Design flow

$$Q = 80000\times 135\times 0.78\times 2.5/1000 = 21060\ \text{m}^3/\text{day}$$

Step 2: Capacity

Adopt detention period $t = 2.0$ h and side water depth $H = 3.0$ m (typical for plain sedimentation: 2-3 h, 2.5-4 m).

$$V = Q\,t = \frac{21060}{24}\times 2.0 = 1755.0\ \text{m}^3,\qquad A = \frac{V}{H} = \frac{1755.0}{3.0} = 585.0\ \text{m}^2$$

Step 3: Diameter

Provide 2 circular tanks, each with area $A_1 = A/2$ (one tank can then be shut down for cleaning).

$$D = \sqrt{\frac{4A_1}{\pi}} = \sqrt{\frac{4\times 292.5}{\pi}} = 19.30\ \text{m}\ \Rightarrow\ \text{adopt } D = 19.5\ \text{m}$$

Adopt a total depth of $H + 0.5\ (\text{free board}) + 0.5\ (\text{sludge zone}) = 4.0$ m, with a central inlet well and a peripheral weir.

Step 4: Checks

$$\begin{aligned} \text{Surface loading} &= \frac{Q/N}{\pi D^2/4} = \frac{10530}{298.6} = 35.3\ \text{m}^3/\text{m}^2\text{/day}\ (\text{usual 25-40 for primary tanks})\\ \text{Weir loading} &= \frac{Q/N}{\pi D} = \frac{10530}{\pi\times 19.5} = 171.9\ \text{m}^3/\text{m/day}\ (\text{should be below about 300})\\ \text{Actual detention} &= \frac{(\pi D^2/4)H}{Q/N}\times 24 = 2.04\ \text{h} \end{aligned}$$

Check: for $0.1<d<1$ mm, Hazen's transition formula at 20°C gives $v_s = 60.6\times1.65\times0.12\times1.3 = 15.6$ mm/s $\approx 1348$ m/day ($d$ in mm). This is far greater than the overflow rate of the tank, so silica of 0.12 mm and larger is removed.

   Section (circular, radial flow)
      inlet well        weir/launder
   ->  |__|~~~~~~~~~~~~~~~~~~~~~|_
       |  \                  /  | H = 3.0 m
       |   \______    ______/   | + sludge zone
       +----------\__/----------+
                  sludge hopper -> sludge pipe
        <---------- D = 19.5 m ---------->

Answer: 2 circular sedimentation tanks, each of diameter 19.5 m, side water depth 3.0 m (total depth about 4.0 m), detention 2.0 h, surface loading 35.3 m³/m²/day.