- 2079 Baisakh · 8 marks
Service reservoir of 30 m diameter, 1,00,000 population
Short answer
Daily demand is 11,000 m³ with uniform inflow 458.33 m³/h. Mass-curve gives maximum deficit 3,483.33 m³, so capacity ≈ 3,483 m³; storage at 12 h is 641.67 m³, giving water level 0.91 m in the 30 m diameter tank.
Determine the capacity of a service reservoir of diameter 30 m for a town having 1,00,000 populations with peak per capita water demand of 110 liters/day. The water demand is to be fulfilled by a river flowing under gravity by a continuous system. The variations of the demand are as follows:
| Time (hours) | 05-07 | 07-12 | 12-17 | 17-19 | 19-05 |
|---|---|---|---|---|---|
| Demand (%) | 25 | 30 | 15 | 20 | 10 |
Also determine the water level in the tank at 12 hrs.
Given data
- Population 100,000 × 110 lpcd = 11,000 m³/day
- River water flows in by gravity at a uniform rate: 11,000/24 = 458.33 m³/h
- Tank diameter = 30 m, area = π × 30²/4 = 706.86 m²
- Demand: 5–7 h 25%, 7–12 h 30%, 12–17 h 15%, 17–19 h 20%, 19–5 h 10%
Mass-curve table (analytical method)
Inflow: 458.33 m³/h for 24 h. Time is counted from the start of the first demand period; a positive cumulative value means surplus in the tank.
| Time | Demand (m³) | Inflow (m³) | Inflow − demand | Cumulative |
|---|---|---|---|---|
| 05:00–07:00 | 2750.00 | 916.67 | -1833.33 | -1833.33 |
| 07:00–12:00 | 3300.00 | 2291.67 | -1008.33 | -2841.67 |
| 12:00–17:00 | 1650.00 | 2291.67 | +641.67 | -2200.00 |
| 17:00–19:00 | 2200.00 | 916.67 | -1283.33 | -3483.33 |
| 19:00–05:00 | 1100.00 | 4583.33 | +3483.33 | 0.00 |
Total demand = 11000.00 m³; total inflow = 11000.00 m³.
Capacity
- Maximum cumulative surplus = 0.00 m³
- Maximum cumulative deficit = 3483.33 m³
- Balancing capacity = max. surplus + max. deficit = 0.00 + 3483.33 = 3483.33 m³
Depth and water level
- Water depth for full capacity m (adopt about 5 m plus 0.5 m free board)
- The reservoir is empty at 19:00 and full at 05:00. At 12:00 the cumulative value is −2,841.67 m³, so storage = −2,841.67 + 3,483.33 = 641.67 m³
- Water level at 12 h m above the floor
Answer: Capacity ≈ 3,483 m³; water level in the tank at 12 h ≈ 0.91 m.
✓ Answer checked by Claude Opus 5.5 (high effort)
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