---
title: "Storage for mean annual flow (monthly volumes)"
subject: "Hydropower Engineering"
chapter: 3
key: "semester_7/hydropower_engineering:storage-capacity-mean-annual-flow-volumes"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/storage-capacity-mean-annual-flow-volumes
site: BCT Engineering
---

# Storage for mean annual flow (monthly volumes)

Hydropower Engineering · Chapter 3: Power and Energy Potential study

- Asked in: 2075 Ashwin, 4 marks
- Video: [Reservoir Planning: Estimating Reservoir Capacity of a Dam Reservoir by ‘Mass Curve’ Method](https://www.youtube.com/watch?v=5Njmy80RSXM) — WIT Solapur - Professional Learning Community
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/storage-capacity-mean-annual-flow-volumes
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-3

## Question

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 |

## 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.

## Answer

The reservoir must supply the **mean flow** as a constant draft, so the storage is the largest cumulative deficit.

Mean monthly volume $=\dfrac{6,671}{12} = 555.9\times10^6$ 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).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What draft is used to find the storage needed to supply the mean annual flow?
   A. The maximum monthly volume
   B. The mean monthly volume (6,671/12 = 555.9 x10^6 m³)
   C. The minimum monthly volume
   D. The volume of the wettest month
   Answer: B. The reservoir supplies the mean flow as a constant draft, so each month's draft is 555.9 x10^6 m³. (Key point: Constant draft at mean flow)

2. Starting with a full reservoir, from which month does the critical cumulative deficit begin?
   A. Month 1, where the first volume is smallest
   B. Month 4, the start of the surplus
   C. Month 9, after the surplus months 4 to 8 fill the reservoir
   D. Month 6, the largest inflow
   Answer: C. Months 4 to 8 are surplus and fill the reservoir; months 9 to 12 and 1 to 3 are deficit months, so the reservoir is full at the start of month 9. (Key point: Which months form the deficit period)

3. What is the required storage and how is it read from the cumulative deficit table?
   A. 1,802 x10^6 m³, the largest cumulative deficit (after month 3)
   B. 207.9 x10^6 m³, the first deficit
   C. 555.9 x10^6 m³, the mean volume
   D. 6,671 x10^6 m³, the annual total
   Answer: A. Storage equals the maximum cumulative deficit, which reaches 1802.4 x10^6 m³ after month 3 of the following year. (Key point: Storage = maximum cumulative deficit)

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