Circular sedimentation tank, population 5500

Assumptions: sewage reaching the plant $=0.75\times 180 = 135$ lpcd, designed for the maximum rate ($2.4\times$ average): $Q_{avg}=5500\times 135/1000 = 742.5$ m³/day. Detention 2 h and depth 3 m are adopted (usual design values). Silica grains of $d=0.14$ mm ($G=2.65$) at 20°C.

Step 1: Design flow

$$Q = 5500\times 180\times 0.75\times 2.4/1000 = 1782\ \text{m}^3/\text{day}$$

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).

$$V = Q\,t = \frac{1782}{24}\times 2.0 = 148.5\ \text{m}^3,\qquad A = \frac{V}{H} = \frac{148.5}{3.0} = 49.5\ \text{m}^2$$

Step 3: Diameter

Provide one circular tank, so $A_1=A$.

$$D = \sqrt{\frac{4A_1}{\pi}} = \sqrt{\frac{4\times 49.5}{\pi}} = 7.94\ \text{m}\ \Rightarrow\ \text{adopt } D = 8.0\ \text{m}$$

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

$$\begin{aligned} \text{Surface loading} &= \frac{Q/N}{\pi D^2/4} = \frac{1782}{50.3} = 35.5\ \text{m}^3/\text{m}^2\text{/day}\ (\text{usual 25-40 for primary tanks})\\ \text{Weir loading} &= \frac{Q/N}{\pi D} = \frac{1782}{\pi\times 8.0} = 70.9\ \text{m}^3/\text{m/day}\ (\text{should be below about 300})\\ \text{Actual detention} &= \frac{(\pi D^2/4)H}{Q/N}\times 24 = 2.03\ \text{h} \end{aligned}$$

Check of removal of the 0.14 mm silica: for $0.1<d<1$ mm, Hazen's transition formula applies: $v_s=60.6(G-1)d\dfrac{3T+70}{100}=60.6\times1.65\times0.14\times1.3 = 18.2$ mm/s $\approx 1572$ m/day ($d$ in mm, $T=20$°C). The tank overflow rate is only 35.5 m³/m²/day, much less than $v_s$, so all silica particles larger than 0.14 mm settle easily; the tank size is governed by the detention time, not by the settling velocity.

   Section (circular, radial flow)
      inlet well        weir/launder
   ->  |__|~~~~~~~~~~~~~~~~~~~~~|_
       |  \                  /  | H = 3.0 m
       |   \______    ______/   | + sludge zone
       +----------\__/----------+
                  sludge hopper -> sludge pipe
        <---------- D = 8.0 m ---------->

Answer: 1 circular sedimentation tank of diameter 8.0 m, side water depth 3.0 m (total depth about 4.0 m), detention 2.0 h, surface loading 35.5 m³/m²/day.