Circular sedimentation tank for 58 MLD

Assumptions: detention 2 h at the design flow of 58 MLD, side water depth 3 m. Two tanks are provided. The particle sizes are not given, so the sizes removed are only checked at the end (20°C, $\nu=1.01\times 10^{-6}$ m²/s).

Step 1: Design flow

$$Q = 58\times 10^6/1000 = 58000\ \text{m}^3/\text{day}$$

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).

$$V = Q\,t = \frac{58000}{24}\times 2.0 = 4833.3\ \text{m}^3,\qquad A = \frac{V}{H} = \frac{4833.3}{3.0} = 1611.1\ \text{m}^2$$

Step 3: Diameter

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

$$D = \sqrt{\frac{4A_1}{\pi}} = \sqrt{\frac{4\times 805.6}{\pi}} = 32.03\ \text{m}\ \Rightarrow\ \text{adopt } D = 32.5\ \text{m}$$

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

$$\begin{aligned} \text{Surface loading} &= \frac{Q/N}{\pi D^2/4} = \frac{29000}{829.6} = 35.0\ \text{m}^3/\text{m}^2\text{/day}\ (\text{usual 25-40 for primary tanks})\\ \text{Weir loading} &= \frac{Q/N}{\pi D} = \frac{29000}{\pi\times 32.5} = 284.0\ \text{m}^3/\text{m/day}\ (\text{should be below about 300})\\ \text{Actual detention} &= \frac{(\pi D^2/4)H}{Q/N}\times 24 = 2.06\ \text{h} \end{aligned}$$

Size of particles removed: the tank removes all particles whose settling velocity is $\ge$ the overflow rate $v_0 = 35.0/86400 = 4.05\times 10^{-4}$ m/s. From Stokes' law, $d=\sqrt{18\nu v_0/(g(G-1))}$:

• inorganic particles ($G=2.65$): $d = 0.021$ mm
• organic particles ($G=1.12$): $d = 0.079$ mm

Particles larger than these are fully removed (Stokes' law is valid, since $Re<1$).

   Section (circular, radial flow)
      inlet well        weir/launder
   ->  |__|~~~~~~~~~~~~~~~~~~~~~|_
       |  \                  /  | H = 3.0 m
       |   \______    ______/   | + sludge zone
       +----------\__/----------+
                  sludge hopper -> sludge pipe
        <---------- D = 32.5 m ---------->

Answer: 2 circular sedimentation tanks, each of diameter 32.5 m, side water depth 3.0 m (total depth about 4.0 m), detention 2.0 h, surface loading 35.0 m³/m²/day.