- 2081 Bhadra · 8 marks
Is reservoir necessary: village of 800, spring 0.5 L/s
Short answer
Daily demand 36 m3, spring yield 43.2 m3/day. Peak demand exceeds inflow, so balancing tank needed. Capacity by mass curve method is 7.2 m3 (adopt 8 m3).
A village has a population of 800, with a per capita water demand of 45 liters per day. The demand is to be met by a continuous supply system from a spring source with a safe yield of 0.5 liters per second. The consumption pattern is
| Time | 00-04 | 04-08 | 08-12 | 12-16 | 16-20 | 20-24 |
|---|---|---|---|---|---|---|
| Demand (million liters) | 5 % | 30 % | 25 % | 10 % | 20 % | 10 % |
Is reservoir necessary? Calculate its capacity if necessary.
Given data
- Population 800, demand 45 lpcd: daily demand = 800 × 45 = 36,000 L = 36 m³/day
- Spring yield = 0.5 lps = 0.5 × 3600 = 1800 L/h = 1.8 m³/h = 43.2 m³/day
- Demand pattern (% of the daily demand) for six 4-hour periods (the table gives % although the heading says million litres)
Check of source and need of storage
The yield of 43.2 m³/day is more than the demand of 36 m³/day, so the source is enough for the whole day. But in 4–8 h the demand is 30% × 36 = 10.8 m³ in 4 h = 2.7 m³/h, and in 8–12 h it is 2.25 m³/h; both exceed the inflow of 1.8 m³/h. Therefore a reservoir is necessary.
Mass-curve table (analytical method)
Inflow: 1.8 m³/h (spring yield). 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 |
|---|---|---|---|---|
| 00:00–04:00 | 1.80 | 7.20 | +5.40 | +5.40 |
| 04:00–08:00 | 10.80 | 7.20 | -3.60 | +1.80 |
| 08:00–12:00 | 9.00 | 7.20 | -1.80 | 0.00 |
| 12:00–16:00 | 3.60 | 7.20 | +3.60 | +3.60 |
| 16:00–20:00 | 7.20 | 7.20 | 0.00 | +3.60 |
| 20:00–00:00 | 3.60 | 7.20 | +3.60 | +7.20 |
Total demand = 36.00 m³; total inflow = 43.20 m³.
Capacity
- Maximum cumulative surplus = 7.20 m³
- Maximum cumulative deficit = 0.00 m³
- Balancing capacity = max. surplus + max. deficit = 7.20 + 0.00 = 7.20 m³
- Because the inflow in a day (43.20 m³) is more than the demand, the extra water simply overflows once the tank is full. The minimum storage that still meets every demand is the largest draw-down, 5.40 m³ (from +5.40 at 04:00 to 0.00 at 12:00). The textbook value of 7.20 m³ is on the safe side.
Answer: A reservoir is necessary; balancing capacity ≈ 7.2 m³ (adopt 8 m³).
✓ Answer checked by Claude Opus 5.5 (high effort)
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