Periodic settling basin with and without turbulence

Given: design discharge $Q=5.0$ m³/s; particles of size $d\ge 0.20$ mm to be trapped, fall velocity $w=6.00$ cm/s $=0.0600$ m/s (given). Periodic (intermittent) flushing is used, so no extra flushing discharge is added; the basin is designed both without and with turbulence.

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):

$$v=44\sqrt{0.20}=19.68\ \text{cm/s}=0.1968\ \text{m/s}$$

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

Take the flow depth $H=2.4$ m in the settling zone (given; sediment storage is extra).

$$B=\frac{Q}{vH}=\frac{5.0}{0.1968\times2.4}=10.59\ \text{m}$$

Provide $n=2$ chambers so that one can be flushed while the other works: $b=B/n=5.29$ m each, adopt 5.5 m.

Step 3: Length without turbulence

$$L_0=\frac{vH}{w}=\frac{0.1968\times2.4}{0.0600}=7.9\ \text{m}$$

Step 4: Effect of turbulence

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

$$\begin{aligned} \alpha&=\frac{0.132\times0.1968}{\sqrt{2.4}}=0.0168\ \text{m/s}\\ w'&=0.0600-0.0168=0.0432\ \text{m/s}\\ L&=\frac{vH}{w'}=\frac{0.1968\times2.4}{0.0432}=10.9\ \text{m} \end{aligned}$$

Adopted dimensions

Total volume of water in the basin $\approx 396$ 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 maintained 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.

Comparison

Turbulence increases the length by 39%; the width (10.59 m in total) and the depth are unchanged. For periodic flushing, a sediment storage depth is added below the settling zone, and each chamber is flushed in turn.

Answer: without turbulence, 2 chambers of 5.5 m x about 8 m x 2.4 m; with turbulence, 2 chambers of 5.5 m x about 11 m x 2.4 m (15 m adopted for safety), with $v=0.197$ m/s.