Settling tank 30 m x 3 m, 0.02 mm, SG 2.50

For 100 % removal in an ideal continuous-flow tank, a particle must settle the full depth during the detention time: $t = H/v_s$.

Detention time

Data: $d = 0.02$ mm $=0.002$ cm, $S_s = 2.50$, $T = 20$ °C, $\nu = 0.01007$ cm²/s, $H = 3.0$ m $= 300$ cm, $L = 30$ m.

$$v_s=\frac{981\times(2.50-1)\times0.002^2}{18\times0.01007}=0.0325\ \text{cm/s}$$

$Re=0.006<1$, so Stokes' law is valid.

$$t=\frac{300}{0.0325}=9239\ \text{s}=2.57\ \text{h}$$

Horizontal velocity $=L/t=3000/9239=0.325$ cm/s ($=0.19$ m/min, below 0.3 m/min).

Answer: recommended detention time = 2.57 h (about 154 min).

Effect of temperature on removal

Settling velocity is inversely proportional to the kinematic viscosity: $v_s \propto 1/\nu$. As the temperature of water falls, the viscosity rises (it is 0.01306 cm²/s at 10 °C and 0.00893 cm²/s at 25 °C), so settling is slower and fewer particles are removed in a given tank. In cold weather the detention time must be longer (or the surface area larger) for the same efficiency. Hence a tank is designed for the lowest water temperature.