- 2075 Ashwin · 4 marks
Storage for mean annual flow (monthly volumes)
Short answer
The mean monthly volume is 555.9×10⁶ m³. The cumulative deficit from September to March reaches a maximum of 1802.4×10⁶ m³. Therefore, the required storage capacity is approximately 1,802×10⁶ m³.
Monthly flow volumes feeding a reservoir are given in the table. Determine the storage capacity required to supply the mean annual flow.
| Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Volume (10⁶ m³) | 296 | 386 | 504 | 714 | 810 | 1154 | 746 | 1158 | 348 | 150 | 223 | 182 |
The reservoir must supply the mean flow as a constant draft, so the storage is the largest cumulative deficit.
Mean monthly volume m³.
| Month | Volume | Mean (draft) | Excess (+) / Deficit (−) |
|---|---|---|---|
| 1 | 296 | 555.9 | -259.9 |
| 2 | 386 | 555.9 | -169.9 |
| 3 | 504 | 555.9 | -51.9 |
| 4 | 714 | 555.9 | +158.1 |
| 5 | 810 | 555.9 | +254.1 |
| 6 | 1154 | 555.9 | +598.1 |
| 7 | 746 | 555.9 | +190.1 |
| 8 | 1158 | 555.9 | +602.1 |
| 9 | 348 | 555.9 | -207.9 |
| 10 | 150 | 555.9 | -405.9 |
| 11 | 223 | 555.9 | -332.9 |
| 12 | 182 | 555.9 | -373.9 |
Months 4 to 8 have a surplus and fill the reservoir. Months 9 to 12 and 1 to 3 (the following year) are deficit months. Cumulative deficit from month 9 (reservoir full at the start of month 9):
| After month | 9 | 10 | 11 | 12 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| Cumulative deficit | 207.9 | 613.8 | 946.7 | 1320.7 | 1580.6 | 1750.5 | 1802.4 |
The maximum cumulative deficit is 1802.4 × 10⁶ m³.
Answer: required storage capacity ≈ 1,802 × 10⁶ m³ (about 1,802 million m³).
✓ Answer checked by Claude Opus 5.5 (high effort)
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