---
title: "Rapid sand filter for 60000 population"
subject: "Water Supply Engineering"
chapter: 6
key: "semester_5/water_supply_engineering:rsf-c69"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/rsf-c69
site: BCT Engineering
---

# Rapid sand filter for 60000 population

Water Supply Engineering · Chapter 6: Water Treatment

- Asked in: 2069 Chaitra, 8 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/rsf-c69
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-6

## Question

Design rapid sand filter for a population of 60000 nos for a newly growing urban area.

## Short answer

Design flow 8262 m³/d. Four beds, each 3.9 m × 4.9 m, total depth 3.4 m. Filter media: 0.7 m sand (effective size 0.5 mm, UC ≤1.5) over 0.45 m graded gravel. Underdrain: 550 mm manifold with 32 laterals of 75 mm, perforated with 507 holes (12 mm dia) per bed.

## Answer

Population 60,000 is taken as the design population for the new urban area. Per capita demand is assumed to be 135 lpcd (urban supply as per Nepal Water Supply Design Guidelines).

#### Step 1: Design flow
- Design population = 60,000 (given)
- Average daily demand $Q = 60,000 \times 135/1000 = 8,100$ m³/day
- Add 2% for wash water: $Q' = 1.02 \times 8,100 = 8,262$ m³/day, i.e. 344.2 m³/h (plant works 24 h/day)

#### Step 2: Plan area and number of beds
- Filtration rate adopted = 4.5 m³/m²/h (4500 L/h/m², usual range 3000–6000)
- Total area $A = 344.2/4.5 = 76.5$ m²
- Number of beds $N = 1.22\sqrt{Q_{MLD}} = 1.22\sqrt{8.10}$ = 3.47, adopt **4 beds** (minimum 4 so that one can be washed while the rest work)
- Area of one bed $= 76.5/4 = 19.12$ m²
- Take $L/B = 1.25$: $B = \sqrt{19.12/1.25} = 3.91$ m. Adopt **B = 3.9 m, L = 4.9 m** (area 19.11 m² each, total 76.44 m²)
- Actual rate with all beds working = 4.50 m/h; with one bed under wash = 6.00 m/h (within 3–6 m/h, OK)

#### Step 3: Filter media (sand and gravel)
| Layer | Size | Depth |
|---|---|---|
| Filter sand | effective size 0.5 mm, UC ≤ 1.5 | 700 mm |
| Gravel layer 4 (top) | 3–6 mm | 100 mm |
| Gravel layer 3 | 6–12 mm | 100 mm |
| Gravel layer 2 | 12–20 mm | 100 mm |
| Gravel layer 1 (bottom) | 20–40 mm | 150 mm |

Gravel (base material) is 450 mm in total. It supports the sand, stops it entering the laterals and spreads the wash water evenly.

#### Step 4: Underdrainage (perforated manifold and laterals)
- Backwash rate = 0.6 m³/min/m² (0.01 m/s) for 10 min, so wash flow per bed $= 0.01 \times 19.11 = 0.191$ m³/s
- Total perforation area = 0.3% of bed area $= 0.003 \times 19.11 = 0.057$ m²
- Perforation diameter 12 mm (area 1.131 cm²): number of holes $= 507$ per bed
- Manifold along the 4.9 m length, laterals at 0.3 m c/c on both sides: $4.9/0.3 \approx 16$ per side, i.e. **32 laterals**, about 16 holes each
- Area of laterals = 2 × perforation area $= 0.115$ m², i.e. $0.115/32 = 0.0036$ m² each, so $D = 68$ mm, adopt **75 mm**; length $\approx (3.9 - 0.55)/2 = 1.68$ m (L/D ≈ 22, below 60, OK)
- Area of manifold = 2 × area of laterals $= 0.229$ m², so $D = 540$ mm, adopt **550 mm**
- Wash velocity in manifold $= 0.191/0.229 = 0.83$ m/s (< 2.5 m/s, OK)

#### Step 5: Depth of the bed
Free board 0.5 m + water depth over sand 1.5 m + sand 0.7 m + gravel 0.45 m + underdrain space 0.25 m = **3.4 m**.

```text
 Inlet  ->  | Free board 0.5 m         |
            |~~~ water 1.5 m ~~~~~~~~~~|--> wash-water
            |__________________________|    trough
            | Sand 0.7 m               |
            | Gravel 0.45 m            |
            |___o_o_o_laterals_o_o_o___|
            |====== manifold ==========|--> filtered
            (3.4 m total depth)          water
```

**Answer: 4 rapid sand filter beds, each 3.9 m × 4.9 m, 3.4 m deep, filtration rate 4.5 m/h, sand 0.7 m on 0.45 m graded gravel, with a perforated underdrain of a 550 mm manifold and 32 laterals of 75 mm.**

## Check yourself

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

1. Why is 135 lpcd used?
   A. It is the fire demand
   B. Urban supply guideline value for the Nepal design guidelines
   C. It is the industrial demand
   D. It is the rural demand
   Answer: B. The question gives no demand, so a guideline urban figure is assumed. (Key point: Assumed demand)

2. With Q = 8.1 MLD, how many beds are adopted?
   A. 4, since 1.22 sqrt(8.1) = 3.47 and 4 is the minimum
   B. 3
   C. 8
   D. 12
   Answer: A. The formula gives 3.47 and the design uses at least four beds. (Key point: Beds)

3. Which check ensures acceptable rate during washing?
   A. 1.5 m/h with one bed under wash
   B. 10 m/h under wash
   C. 6.00 m/h with one bed under wash, within 3 to 6 m/h
   D. 0.2 m/h under wash
   Answer: C. With 3 beds sharing the flow, the rate rises from 4.5 to 6 m/h. (Key point: Rate with wash)

4. What is the filter sand specification?
   A. Effective size 0.2 mm, UC 4, 900 mm
   B. Effective size 5 mm, UC 3, 300 mm
   C. Effective size 0.5 mm, UC 6, 70 mm
   D. Effective size 0.5 mm, UC 1.5 or less, 700 mm deep
   Answer: D. Rapid filters use coarser, more uniform sand than slow filters. (Key point: Sand specification)

## Related in Water Supply Engineering

- [Rapid sand filter design, 50,000 population](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Arsf-c72) — 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
- [Rapid sand filter design for 25 MLD](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Arsf-b81) — Water Supply Engineering, chapter 6
- [Rapid sand filter construction and working](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Arsf-construction-working) — Water Supply Engineering, chapter 6, asked 5×
- [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
- [Rapid sand filter for 5000 persons](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Arsf-k78) — Water Supply Engineering, chapter 6

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