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Slow sand filter, 35,000 in 2019 for 2039

Short answer

Design population 79,693, flow 15,939 m³/d at 0.2 m³/m²/h. Use 34 working plus 1 standby units, each7.0 m ×14.0 m (98.0 m²), total depth2.7 m (free board0.3 m, water1.0 m, sand0.9 m, gravel0.3 m, underdrain0.2 m).

A town with population of 35,000 in the year 2019 AD has a water supply rate of 200 lpcd. Determine the number and dimensions of the slow sand filter for the design year 2039. Assume that annual population growth rate of the town is 4.2%. Sketch with showing each components.

Design year 2039 is 20 years after 2019. A filtration rate of 0.2 m³/m²/h is assumed.

Step 1: Design flow

  • Population forecast (geometric increase): Pn=P0(1+r)n=35,000×(1+0.042)20=79,693P_n = P_0(1+r)^n = 35,000\times(1+0.042)^{20} = 79,693 (2019 to 2039)
  • Daily demand Q=79,693×200/1000=15,938.7Q = 79,693 \times 200/1000 = 15,938.7 m³/day = 664.11 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)=664.11/0.2=3320.6A = Q/(\text{rate}) = 664.11/0.2 = 3320.6 m²
  • Keep each unit below about 100 m² and use at least 2 working units: working units n = 34, plus 1 standby unit for cleaning, so 35 units in all
  • Area of one unit =3320.6/34=97.7= 3320.6/34 = 97.7 m²
  • Take L=2BL = 2B: B=97.7/2=6.99B = \sqrt{97.7/2} = 6.99 m. Adopt B = 7.0 m, L = 14.0 m (area 98.0 m² each)
  • Check: rate with 34 working units = 0.199 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: 34 working + 1 standby slow sand filters, each 7.0 m × 14.0 m (98.0 m²), total depth about 2.7 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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