Rectangular grit chamber for 10 MLD

Grit particles of $d=0.2$ mm and $G=2.65$ are to be removed from the maximum flow of 10 MLD. The settling velocity ($0.02$ m/s) and the flow velocity ($0.3$ m/s, maintained constant by a proportional weir at the outlet) are given. $k=0.06$ and $f=0.03$ are assumed only for the scour check.

Step 1: Design flow

$$Q = \frac{10\times 10^6}{1000\times 86400} = 0.1157\ \text{m}^3/\text{s}$$

Step 2: Settling velocity of the grit

The settling velocity is given: $v_s = 0.02$ m/s.

Step 3: Horizontal (flow-through) velocity

The velocity must not scour settled grit. Scour (critical) velocity (Camp-Shields):

$$v_c = \sqrt{\frac{8k}{f}(G-1)\,g\,d} = \sqrt{\frac{8\times 0.06}{0.03}(2.65-1)\times 9.81\times 0.2\times 10^{-3}} = 0.228\ \text{m/s}$$

The flow velocity is given: $v_h = 0.3$ m/s. (It is slightly above the Camp-Shields scour value for 0.2 mm grit, but a proportional weir holds it constant and the usual 0.3 m/s limit applies.)

Step 4: Cross-section and dimensions

$$\begin{aligned} A_c &= \frac{Q}{v_h} = \frac{0.1157}{0.30} = 0.386\ \text{m}^2\\ \text{Adopt depth } H &= 0.6\ \text{m} \Rightarrow B = \frac{A_c}{H} = 0.64\ \text{m (adopt 0.7 m)}\\ L_{theo} &= \frac{v_h H}{v_s} = \frac{0.30\times 0.6}{0.0200} = 9.00\ \text{m}\\ L &= \max(1.25\,L_{theo},\ 30\,v_h) = \max(11.25,\ 9.00) = 11.25\ \text{m (adopt 11.5 m)} \end{aligned}$$

(25% is added for inlet and outlet turbulence, and the length is not allowed to give less than 30 s detention.)

Step 5: Checks

$$\begin{aligned} \text{Detention time} &= \frac{L}{v_h} = \frac{11.5}{0.30} = 38\ \text{s}\ (\text{within 30-90 s})\\ \text{Surface loading} &= \frac{Q}{B\,L} = \frac{0.1157\times 86400}{0.7\times 11.5} = 1242\ \text{m}^3/\text{m}^2\text{/day} \end{aligned}$$

Total depth $= H + \text{grit storage } 0.25 + \text{free board } 0.30 = 1.15$ m.

 Plan:   inlet ->[ <-- L = 11.5 m --> ]-> outlet (weir)
                 |  B = 0.7 m          |
 Section: water level ~~~~~~~~~~~~~~~~~~~  H = 0.6 m
          grit storage 0.25 m  ______________

Answer: provide a grit chamber (at least two units in parallel, each for the full flow so that one can be cleaned) of size $L\times B\times H = 11.5\ \text{m}\times 0.7\ \text{m}\times 0.6\ \text{m}$ (water depth), total depth about 1.15 m, with flow velocity 0.30 m/s.