---
title: "Slow sand filter, 35,000 in 2019 for 2039"
subject: "Water Supply Engineering"
chapter: 6
key: "semester_5/water_supply_engineering:ssf-c75"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ssf-c75
site: BCT Engineering
---

# Slow sand filter, 35,000 in 2019 for 2039

Water Supply Engineering · Chapter 6: Water Treatment

- Asked in: 2075 Chaitra, 6+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ssf-c75
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-6

## Question

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.

## 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).

## Answer

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): $P_n = P_0(1+r)^n = 35,000\times(1+0.042)^{20} = 79,693$ (2019 to 2039)
- Daily demand $Q = 79,693 \times 200/1000 = 15,938.7$ 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 $A = Q/(\text{rate}) = 664.11/0.2 = 3320.6$ 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 $= 3320.6/34 = 97.7$ m²
- Take $L = 2B$: $B = \sqrt{97.7/2} = 6.99$ 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
| Component | Depth |
|---|---|
| Free board | 0.3 m |
| Supernatant water | 1.0 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 |
| **Total** | **2.7 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

```text
 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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is n for 2019 to 2039?
   A. 10 years
   B. 20 years
   C. 40 years
   D. 2039 years
   Answer: B. 2039 - 2019 = 20. (Key point: Design period)

2. How is the total filter area found?
   A. A = Q (m^3/h) / rate = 664.11/0.2 = 3320 m^2
   B. A = Q × rate
   C. A = Q/24 × 0.2
   D. A = Q/ 3
   Answer: A. Total area is flow divided by filtration rate. (Key point: Area)

3. Why 34 working units?
   A. Rate must be 34 m/h
   B. The population is 34 000
   C. Each unit is kept near or below about 100 m^2
   D. The sand is 34 cm deep
   Answer: C. 3320.6/34 = 97.7 m^2 per unit. (Key point: Unit size limit)

4. What shape is used?
   A. Square
   B. Length half the width
   C. Length equals depth
   D. Length twice the width, B = 7.0 m, L = 14.0 m
   Answer: D. With L = 2B, B = sqrt(A/2). (Key point: Layout ratio)

## Related in Water Supply Engineering

- [Slow sand filter, 10000 pop, 1.5% growth](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Assf-a74) — Water Supply Engineering, chapter 6
- [Slow sand filter, 10000 population, base year 2068](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Assf-bk68) — Water Supply Engineering, chapter 6
- [Slow sand filter, 15000 present population](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Assf-c76) — Water Supply Engineering, chapter 6
- [Slow sand filter, 15,000 population, 150 L/h/m2](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Assf-a75) — Water Supply Engineering, chapter 6
- [Rapid sand filter, 45,000 population in 2021](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Arsf-a76) — Water Supply Engineering, chapter 6
- [Slow sand filter for 3500 population](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Assf-c70o) — Water Supply Engineering, chapter 6

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