- Asked 2/30
- 2070 Chaitra (old course)
Balancing reservoir, town of 1.3 million
Short answer
The balancing reservoir capacity is 45,100 m³, obtained as the sum of maximum cumulative surplus (21,450 m³) and maximum cumulative deficit (23,650 m³) from the mass curve of uniform 13-h pumping at 11,000 m³/h against the hourly demand pattern.
A newly established town with a population of 1.3 million is to be supplied with water daily at 110 liters per head. The variation in demand is as follows.
| Time | Consumption % |
|---|---|
| 05.00-10.00 | 55 |
| 10.00-14.00 | 10 |
| 14.00-18.00 | 20 |
| 18.00-22.00 | 10 |
| 22.00-05.00 | 5 |
Determine analytically the balancing reservoir capacity assuming pumping to be done at a uniform rate and the period of pumping is 5 A.M to 6 P.M. Neglect fire demand.
Given data
- Population 1,300,000 × 110 lpcd = 143,000 m³/day
- Pumping at a uniform rate from 5 AM to 6 PM (13 h): rate = 143,000/13 = 11,000 m³/h
- Fire demand neglected
Mass-curve table (analytical method)
Inflow: 11,000 m³/h during 5–18 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 |
|---|---|---|---|---|
| 05:00–10:00 | 78650.00 | 55000.00 | -23650.00 | -23650.00 |
| 10:00–14:00 | 14300.00 | 44000.00 | +29700.00 | +6050.00 |
| 14:00–18:00 | 28600.00 | 44000.00 | +15400.00 | +21450.00 |
| 18:00–22:00 | 14300.00 | 0.00 | -14300.00 | +7150.00 |
| 22:00–05:00 | 7150.00 | 0.00 | -7150.00 | +0.00 |
Total demand = 143000.00 m³; total inflow = 143000.00 m³.
Capacity
- Maximum cumulative surplus = 21450.00 m³
- Maximum cumulative deficit = 23650.00 m³
- Balancing capacity = max. surplus + max. deficit = 21450.00 + 23650.00 = 45100.00 m³
Answer: Balancing reservoir capacity = 45,100 m³ (31.5% of the daily demand).
✓ Answer checked by Claude Opus 5.5 (high effort)
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