- 2074 Asoj · 8 marks
Storage for uniform inflow over 24 hours
Short answer
Assuming the unclear demand values are 0.67 and 1.33 ML, total demand is 4.84 ML and uniform inflow is 0.2017 ML/h. Mass-curve gives maximum surplus 0.46 ML and maximum deficit 0.27 ML, so storage required ≈ 0.73 ML (730 m³).
Calculate the storage required to supply the demand shown in the following table if the inflow of water to the reservoir is maintained at a uniform rate throughout 24 hours.
| Time (hours) | 00-04 | 04-08 | 08-12 | 12-16 | 16-20 | 20-24 |
|---|---|---|---|---|---|---|
| Demand (million litres) | 0.48 | 0.[?]7 | 1.[?]3 | 1.00 | 0.82 | 0.54 |
Given data
- Demand in million litres for six 4-hour periods: 0.48, 0.67, 1.33, 1.00, 0.82, 0.54
- Two digits are unclear in the question paper; they are read as 0.67 and 1.33. Total demand = 4.84 ML
- Inflow is uniform over 24 h: 4.84/24 = 0.2017 ML/h = 0.8067 ML per 4 h
Mass-curve table (analytical method)
Inflow: 0.807 ML per 4-hour period. Time is counted from the start of the first demand period; a positive cumulative value means surplus in the tank.
| Time | Demand (ML) | Inflow (ML) | Inflow − demand | Cumulative |
|---|---|---|---|---|
| 00:00–04:00 | 0.48 | 0.81 | +0.33 | +0.33 |
| 04:00–08:00 | 0.67 | 0.81 | +0.14 | +0.46 |
| 08:00–12:00 | 1.33 | 0.81 | -0.52 | -0.06 |
| 12:00–16:00 | 1.00 | 0.81 | -0.19 | -0.25 |
| 16:00–20:00 | 0.82 | 0.81 | -0.01 | -0.27 |
| 20:00–00:00 | 0.54 | 0.81 | +0.27 | -0.00 |
Total demand = 4.84 ML; total inflow = 4.84 ML.
Capacity
- Maximum cumulative surplus = 0.46 ML
- Maximum cumulative deficit = 0.27 ML
- Balancing capacity = max. surplus + max. deficit = 0.46 + 0.27 = 0.73 ML
Answer: Storage required ≈ 0.73 ML (730 m³). If the unclear digits are different, repeat the same table with the correct values: capacity = maximum surplus + maximum deficit of the cumulative column.
✓ Answer checked by Claude Opus 5.5 (high effort)
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