Settling basin with Hazen coefficient and sediment depth

Given: particle diameter $d=6$ mm $=0.6$ cm, $s=2.65$, $\mu=1.34$ g/cm·s, $T=20^\circ$C, $Q=12$ m³/s, concentration 5000 ppm (5 kg/m³), flushing discharge 15%, Hazen's performance coefficient $n=0.16$.

Assumptions: required trap efficiency $\eta=90\%$; sediment bulk density 1325 kg/m³ (packing factor 0.5 of 2650 kg/m³); the basin is flushed every 1 hour; horizontal velocity not more than 0.3 m/s; $L/B=4$.

Step 1: Fall velocity (Stokes, with the data given)

$$w=\frac{g\,d^2(\rho_s-\rho)}{18\mu}=\frac{981\times0.6^2\times(2.65-1)}{18\times1.34}=24.16\ \text{cm/s}=0.2416\ \text{m/s}$$

Step 2: Design flow with flushing

$$Q'=1.15\times12=13.8\ \text{m}^3/\text{s}$$

Step 3: Surface area (Hazen)

Hazen's relation for the fraction removed is $\;1-\eta=\left[1+n\dfrac{w\,A}{Q'}\right]^{-1/n}$, so

$$A=\frac{Q'}{n\,w}\left[(1-\eta)^{-n}-1\right]=\frac{13.8}{0.16\times0.2416}\left[(0.1)^{-0.16}-1\right]=159.0\ \text{m}^2$$

This is the minimum surface area.

Step 4: Cross-section and plan size

To stop the settled sediment from being scoured, the horizontal velocity is limited to 0.3 m/s:

$$A_c=\frac{Q'}{v}=\frac{13.8}{0.3}=46\ \text{m}^2$$

With $L/B=4$, adopt $B=8$ m, flow depth $H=6$ m and $L=32$ m:

$$v=\frac{13.8}{8\times6}=0.29\ \text{m/s}\ (\text{OK}),\qquad A=8\times32=256\ \text{m}^2>159\ \text{m}^2\ (\text{OK})$$

(A shallow 2 m deep basin of the Hazen area alone would give $v\approx1$ m/s, which is far too fast.)

Trap efficiency of the adopted basin:

$$\eta=1-\left[1+0.16\times\frac{0.2416\times256}{13.8}\right]^{-1/0.16}=1-(1.717)^{-6.25}=96.6\%$$

Step 5: Depth of sediment

Concentration $5000$ ppm $=5$ kg/m³. Sediment trapped per hour:

$$M=\eta\,C\,Q'\,t=0.966\times5\times13.8\times3600=239930\ \text{kg}$$ $$V_s=\frac{M}{1325}=181.1\ \text{m}^3,\qquad h_s=\frac{V_s}{A}=\frac{181.1}{256}=0.71\ \text{m}$$

So the sediment builds up to about 0.71 m depth in one hour. A hopper depth of about 1.0 m is therefore provided, and the basin must be flushed at least once every hour (or continuously, using the 15% flushing discharge).

PLAN (flushing gate at the downstream end)
          inlet           settling basin            outlet
 canal   transition  +========================+   transition
 =====>  \  guide  / |                        | \  weir   /===> to
         /  vanes  \ |   8 m wide x 32 m long | /         \    headrace
                     +========================+
  trash-                          |  flush gate
  rack                            v  --> flushing channel --> river

LONGITUDINAL SECTION
 inlet          settling zone (H = 6 m)       outlet
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  WL
 \    --->   --->   --->   --->   --->   --->  |
  \  ______________________________________   | weir
   \/   sediment hopper (about 1.0 m)        \__|__ to headrace
          flush gate -> flushing channel -> river

Answer: basin about 8 m wide x 32 m long x 6 m flow depth (plus a 1.0 m hopper), $v=0.29$ m/s, trap efficiency about 96.6%; the sediment depth is about 0.71 m per hour of operation.

Note: the 6 mm size and the viscosity of 1.34 g/cm·s are used exactly as given (water at 20°C actually has $\mu\approx0.01$ g/cm·s). Stokes' law is not strictly valid for such large particles, so the fall velocity is only indicative.