Settling basin 8 m³/s, 0.3 mm, 90% trap

Given: design discharge $Q=8.0$ m³/s; particles of size $d\ge 0.30$ mm to be trapped, fall velocity $w=4.00$ cm/s $=0.0400$ m/s (assumed for 0.3 mm quartz at about 20 °C, after Rouse). The required trap efficiency is 90%, and turbulence is considered.

Step 1: Horizontal velocity (Camp)

For $0.1<d<1$ mm, $v=a\sqrt d$ with $a=44$ (v in cm/s, d in mm):

$$v=44\sqrt{0.30}=24.10\ \text{cm/s}=0.2410\ \text{m/s}$$

This is within the usual 0.1-0.4 m/s range, so deposited sediment is not re-suspended.

Step 2: Cross-section and width

Assume a flow depth $H=3.5$ m in the settling zone (sediment storage is extra).

$$B=\frac{Q}{vH}=\frac{8.0}{0.2410\times3.5}=9.48\ \text{m}$$

Provide $n=2$ chambers so that one can be flushed while the other works: $b=B/n=4.74$ m each, adopt 5.0 m.

Step 3: Length without turbulence

$$L_0=\frac{vH}{w}=\frac{0.2410\times3.5}{0.0400}=21.1\ \text{m}$$

Step 4: Effect of turbulence

Turbulence reduces the effective fall velocity: $w'=w-\alpha$, with $\alpha=0.132\,v/\sqrt{H}$.

$$\begin{aligned} \alpha&=\frac{0.132\times0.2410}{\sqrt{3.5}}=0.0170\ \text{m/s}\\ w'&=0.0400-0.0170=0.0230\ \text{m/s}\\ L&=\frac{vH}{w'}=\frac{0.2410\times3.5}{0.0230}=36.7\ \text{m} \end{aligned}$$

For a trap efficiency of 90% (Vetter's relation $\eta=1-e^{-w'L/(vH)}$), the length is multiplied by $\ln\frac{1}{1-\eta}=2.303$:

$$L=2.303\times36.7=84.5\ \text{m}$$

(This is conservative; Vetter's relation with the still-water fall velocity $w$ alone would give $2.303\times21.1=48.6$ m.)

Adopted dimensions

Total volume of water in the basin $\approx 2\times5\times85\times3.5=2975$ m³.

PLAN (flushing gates at the downstream end)
          inlet        settling chambers      outlet
 canal   transition  +=================+   transition
 =====>  \         / |  chamber 1      | \         /===> to
         /  guide  \ +-----------------+ /  weir   \    headrace
 =====>  \  vanes  / |  chamber 2      | \         /
         /         \ +=================+ /         \
  trash-                  |  |  flush gates
  rack                    v  v  --> flushing channel --> river

LONGITUDINAL SECTION
 inlet          settling zone (depth H)      outlet
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  WL
 \    --->   --->   --->   --->   --->   --->  |
  \  ______________________________________   | weir
   \/   sediment storage / hopper slope 1:30 \__|__ to headrace
          flush gate -> flushing channel -> river

Flushing arrangement: the floor of each chamber slopes at about 1:30-1:50 to a longitudinal flushing channel with a flushing gate at the downstream end. A flushing velocity of at least 3 m/s is kept in the channel. The chamber to be flushed is closed at the inlet, drained and flushed to the river, while the other chamber continues to supply the plant.

Answer: 2 chambers, each about 5.0 m wide x 85 m long x 3.5 m deep (settling zone), with $v=0.241$ m/s.