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Slow sand filter, 15000 present population

Short answer

Design population 24,579, flow 1106 m³/d at 0.2 m³/m²/h. Use 3 working plus 1 standby beds, each 6.2 m × 12.4 m (76.9 m²), total depth 2.7 m (free board 0.3 m, water 1.0 m, sand 0.9 m, gravel 0.3 m, underdrain 0.2 m).

Determine the size of slow sand filter for a present population of 15000 nos, design period = 20 yrs, annual population growth rate = 2.5%, water consumption = 45 lpcd, and also draw the section of slow sand filter.

The design population is found for the end of the 20-year design period. A filtration rate of 0.2 m³/m²/h is assumed.

Step 1: Design flow

  • Population forecast (geometric increase): Pn=P0(1+r)n=15,000×(1+0.025)20=24,579P_n = P_0(1+r)^n = 15,000\times(1+0.025)^{20} = 24,579
  • Daily demand Q=24,579×45/1000=1,106.1Q = 24,579 \times 45/1000 = 1,106.1 m³/day = 46.09 m³/h

Step 2: Area and number of units

  • Filtration rate = 0.2 m³/m²/h (range for slow sand filters 0.1–0.4)
  • Total area A=Q/(rate)=46.09/0.2=230.4A = Q/(\text{rate}) = 46.09/0.2 = 230.4 m²
  • Keep each unit below about 100 m² and use at least 2 working units: working units n = 3, plus 1 standby unit for cleaning, so 4 units in all
  • Area of one unit =230.4/3=76.8= 230.4/3 = 76.8 m²
  • Take L=2BL = 2B: B=76.8/2=6.20B = \sqrt{76.8/2} = 6.20 m. Adopt B = 6.2 m, L = 12.4 m (area 76.9 m² each)
  • Check: rate with 3 working units = 0.200 m/h (OK)

Step 3: Depth of unit

ComponentDepth
Free board0.3 m
Supernatant water1.0 m
Filter sand (effective size 0.2–0.3 mm, UC 3–5)0.9 m
Gravel in 3 layers (3–6, 6–12, 12–40 mm)0.3 m
Under-drain space (central drain and laterals)0.2 m
Total2.7 m

Sand is scraped 15–25 mm every 1–2 months; when its depth falls to 0.5 m it is topped up to 0.9 m. Inlet and outlet chambers, a filtered-water weir, a drain valve and a filter-to-waste connection complete each unit.

Step 4: Section

 inlet -> |  free board 0.3 m             |
          |~~~~ supernatant water 1.0 m ~~|
          |-------------------------------|
          |  filter sand 0.9 m            |
          |-------------------------------|
          |  gravel 0.3 m (3 layers)      |
          |==o==o== under-drain 0.2 m ==o=|
                       |
          outlet weir -> filtered water tank

Answer: 3 working + 1 standby slow sand filters, each 6.2 m × 12.4 m (76.9 m²), total depth about 2.7 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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