Settling basin 40 m³/s, 0.15 mm

Given: design discharge $Q=40.0$ m³/s; particles of size $d\ge 0.15$ mm to be trapped, fall velocity $w=1.50$ cm/s $=0.0150$ m/s (given). Turbulence is considered; the plan and both sections are sketched.

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 $H=5.0$ m in the settling zone (sediment storage is extra).

$$B=\frac{Q}{vH}=\frac{40.0}{0.1704\times5.0}=46.95\ \text{m}$$

Provide $n=3$ chambers so that one can be flushed while the others work: $b=B/n=15.65$ m each, adopt 16.0 m.

Step 3: Length without turbulence

$$L_0=\frac{vH}{w}=\frac{0.1704\times5.0}{0.0150}=56.8\ \text{m}$$

Step 4: Effect of turbulence

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

$$\begin{aligned} \alpha&=\frac{0.132\times0.1704}{\sqrt{5.0}}=0.0101\ \text{m/s}\\ w'&=0.0150-0.0101=0.0049\ \text{m/s}\\ L&=\frac{vH}{w'}=\frac{0.1704\times5.0}{0.0049}=172.5\ \text{m} \end{aligned}$$

Adopted dimensions

Total volume of water in the basin $\approx 42000$ m³.

PLAN (flushing gates at the downstream end)
          inlet        settling chambers      outlet
 canal   transition  +=================+   transition
 =====>  \         / |  chamber 1      | \         /===> to
         /  guide  \ +-----------------+ /  weir   \    headrace
 =====>  \  vanes  / |  chamber 2      | \         /
         /         \ +-----------------+ /         \
                     |  chamber 3      |
                     +=================+
  trash-                  |  |  |  flush gates
  rack                    v  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

CROSS-SECTION (across the three chambers)
      |<-- 16.0 m -->|<-- 16.0 m -->|<-- 16.0 m -->|
  WL ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  free board 0.5 m
      |              |              |              |   ^
      |  chamber 1   |  chamber 2   |  chamber 3   |   | H = 5.0 m
      |              |              |              |   v
      \              /\             /\             /   ^ sediment storage
       \____    ____/  \____  ____/  \____    ____/    v (hopper, ~1.0 m)
            |__|            |__|          |__|
       flushing channel under each chamber (to its flush gate)

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 chambers continue to supply the plant.

Answer: 3 chambers, each about 16.0 m wide x 175 m long x 5.0 m deep (settling zone), with $v=0.170$ m/s.