Rapid sand filter design for 25 MLD

Design data (assumed)

• Flow $Q=25$ MLD $=25\,000$ m³/day
• Rate of filtration 5 m/h $=120$ m³/m²/day (range 3 to 6 m/h)
• 4 % of the filtered water is used for backwashing
• Operation 24 h/day; $L:B=1.25$ (1.25 to 1.33)

Step 1: Design flow and total filter area

$$Q'=25\,000\times1.04=26000\ \text{m}^3/\text{day}=1083.3\ \text{m}^3/\text{h}$$ $$A_{total}=\frac{Q'}{\text{rate}}=\frac{1083.3}{5}=216.7\ \text{m}^2$$

Step 2: Number and size of units

$N=1.22\sqrt{Q}$ (Q in MLD) $=1.22\sqrt{25}=6.1$. Adopt 6 units (plus 1 standby).

$$A_{unit}=\frac{216.7}{6}=36.11\ \text{m}^2,\qquad B=\sqrt{\frac{36.11}{1.25}}=5.37\ \text{m},\quad L=1.25B$$

Adopt $B=5.4$ m, $L=6.7$ m ($A=36.18$ m²). Check: actual rate $=1083.3/(6\times36.18)=4.99$ m/h; when one unit is being washed, the rate in the other 5 is 5.99 m/h (acceptable, close to 6 m/h).

Step 3: Depth of the unit

Step 4: Under-drainage

• Perforated area $=0.3\%$ of bed area $=0.003\times36.18=0.109$ m². With 12 mm orifices (area $1.13\times10^{-4}$ m²): 960 orifices.
• Central manifold along the length, with laterals on both sides at 0.3 m c/c: 44 laterals, about 22 holes each.
• Total lateral area $\approx2\times$ orifice area $=0.217$ m²; manifold area $\approx2\times$ lateral area $=0.434$ m² (diameter about 0.74 m).

Step 5: Backwash

Rate 0.6 m/min (36 m/h) for 10 min: flow $=0.6\times36.18/60=0.362$ m³/s; volume per wash $=217$ m³ per unit, which is about 5 % of a unit's daily output ($26\,000/6=4333$ m³/day). Wash-water troughs are provided above the sand.

 SECTION (one unit)
  inlet                           wash-water trough
    |      _____________________________|__
    v     |  FB 0.5 m                       |
    ----> |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~| water 1.5 m
          |.................................|
          |   sand 0.7 m                    |
          |---------------------------------|
          |   gravel 0.45 m                 |
          |---+----+----+----+----+----+----|
          |   laterals (0.3 m) / manifold   | -> filtered
          |_________________________________|    water out
              wash-water in ^   wash waste out ->

Answer: 6 rapid sand filters (+1 standby), each 6.7 m $\times$ 5.4 m in plan and about 3.45 m deep.