Continuous settling basin (10 m³/s)

Given: design discharge $Q=10.0$ m³/s; particles of size $d\ge 0.15$ mm to be trapped, fall velocity $w=5.00$ cm/s $=0.0500$ m/s (given). The basin is of the continuous flushing type, so a flushing discharge of 10% (1.0 m³/s) is added. Turbulence is included, and other data are assumed. (A fall velocity of 5 cm/s is high for 0.15 mm sand, so the basin is short; the given value is used.)

Flushing water of 10% is added for continuous flushing, so the design flow of the basin is $Q'=10.0+1.0=11.0$ m³/s.

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):

$$v=44\sqrt{0.15}=17.04\ \text{cm/s}=0.1704\ \text{m/s}$$

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 $H=3.0$ m in the settling zone (the hopper depth is extra).

$$B=\frac{Q'}{vH}=\frac{11.0}{0.1704\times3.0}=21.52\ \text{m}$$

Provide $n=2$ chambers, so that one can be taken out for inspection while the other works: $b=B/n=10.76$ m each, adopt 11.0 m.

Step 3: Length without turbulence

$$L_0=\frac{vH}{w}=\frac{0.1704\times3.0}{0.0500}=10.2\ \text{m}$$

Step 4: Effect of turbulence

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

$$\begin{aligned} \alpha&=\frac{0.132\times0.1704}{\sqrt{3.0}}=0.0130\ \text{m/s}\\ w'&=0.0500-0.0130=0.0370\ \text{m/s}\\ L&=\frac{vH}{w'}=\frac{0.1704\times3.0}{0.0370}=13.8\ \text{m} \end{aligned}$$

Adopted dimensions

Total volume of water in the basin $\approx 990$ m³. Because the basin is short and wide, a good inlet transition with guide vanes is essential to spread the flow evenly.

PLAN (continuous flushing outlets along each chamber)
          inlet        settling chambers      outlet
 canal   transition  +=================+   transition
 =====>  \         / |  chamber 1      | \         /===> to
         /  guide  \ +-----------------+ /  weir   \    headrace
 =====>  \  vanes  / |  chamber 2      | \         /
         /         \ +=================+ /         \
  trash-                  |  |  flushing conduits (0.5 m3/s each)
  rack                    v  v  --> flushing channel --> river

LONGITUDINAL SECTION
 inlet          settling zone (depth H)      outlet
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  WL
 \    --->   --->   --->   --->   --->   --->  |
  \  ______________________________________   | weir
   \/ \/ \/ \/ \/ \/ hoppers with bottom outlets \__|__ to headrace
   ==== flushing conduit (continuous flow) ====> river

Flushing arrangement: the floor of each chamber is formed into hoppers with bottom openings leading to a flushing conduit. About 0.5 m³/s per chamber (1.0 m³/s in total) is drawn off continuously through these openings and carries the settled sediment back to the river, so the chambers do not have to be taken out of service for flushing. A gate on each conduit controls the flushing flow, and inlet gates allow one chamber to be isolated for inspection while the other keeps supplying the plant.

Answer: 2 chambers, each about 11.0 m wide x 15 m long x 3.0 m deep (settling zone), with $v=0.170$ m/s and 1.0 m³/s of continuous flushing water.