---
title: "Uniform draw-off and reservoir capacity"
subject: "Hydropower Engineering"
chapter: 3
key: "semester_7/hydropower_engineering:uniform-drawoff-driest-year-reservoir"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/uniform-drawoff-driest-year-reservoir
site: BCT Engineering
---

# Uniform draw-off and reservoir capacity

Hydropower Engineering · Chapter 3: Power and Energy Potential study

- Asked in: 2076 Chaitra, 7+3+2 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/uniform-drawoff-driest-year-reservoir
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-3

## Question

The monthly flows of a stream over the period of the driest year on record are as shown below:

| Month | J | F | M | A | M | J | J | A | S | O | N | D |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Flow (×10⁶ m³) | 4.0 | 2.25 | 5.0 | 1.25 | 0.5 | 0.75 | 0.5 | 0.75 | 1.25 | 1.25 | 5.0 | 6.25 |

(i) Estimate the maximum possible uniform draw-off from this stream and determine the reservoir capacity to achieve the uniform draw-off and the minimum initial storage to maintain the demand.
(ii) If the reservoir has only a total capacity of 8×10⁶ m³ with an initial storage of 4×10⁶ m³, determine (a) the maximum possible uniform draw-off and (b) the spillage.

## Short answer

Total inflow of the driest year is 28.75×10⁶ m³; maximum uniform draw-off is 2.396×10⁶ m³/month, requiring a reservoir capacity of 10.52×10⁶ m³ and minimum initial storage of 6.46×10⁶ m³. With a capacity of 8×10⁶ m³ and initial storage of 4×10⁶ m³, the maximum draw-off is 2.036×10⁶ m³/month and annual spillage is 1.143×10⁶ m³.

## Answer

Volumes are in 10⁶ m³ per month.

#### (i) Maximum uniform draw-off, reservoir capacity, minimum initial storage
Total inflow of the driest year $=28.75$. The maximum uniform draw-off possible in the year is the mean monthly inflow:

$$
x = \frac{28.75}{12} = 2.396\times10^6\ \text{m}^3/\text{month}
$$

Mass-curve table (cumulative of inflow − draw-off, starting from January):

| Month | Inflow | Draw-off | Net | Cumulative |
|---|---|---|---|---|
| J | 4.0 | 2.396 | +1.604 | +1.604 |
| F | 2.25 | 2.396 | -0.146 | +1.458 |
| M | 5.0 | 2.396 | +2.604 | +4.062 |
| A | 1.25 | 2.396 | -1.146 | +2.917 |
| M | 0.5 | 2.396 | -1.896 | +1.021 |
| J | 0.75 | 2.396 | -1.646 | -0.625 |
| J | 0.5 | 2.396 | -1.896 | -2.521 |
| A | 0.75 | 2.396 | -1.646 | -4.167 |
| S | 1.25 | 2.396 | -1.146 | -5.313 |
| O | 1.25 | 2.396 | -1.146 | -6.458 |
| N | 5.0 | 2.396 | +2.604 | -3.854 |
| D | 6.25 | 2.396 | +3.854 | -0.000 |

- The cumulative reaches its **highest** value (+4.062) at the end of March and its **lowest** (-6.458) at the end of October.
- **Minimum initial storage** (January 1st) needed so that the demand is never short: $6.458\times10^6$ m³.
- **Reservoir capacity** = peak − trough $=4.062-(-6.458) = 10.521\times10^6$ m³.

#### (ii) Capacity 8 × 10⁶ m³, initial storage 4 × 10⁶ m³
The reservoir is smaller than 10.52, so some water is spilled when it is full and the draw-off must be reduced so that the storage never becomes negative. Trial routing gives the largest draw-off for which the reservoir just reaches zero (in October):

| Month | Inflow | Draw-off | Storage before spill | Spill | Storage end |
|---|---|---|---|---|---|
| J | 4.0 | 2.036 | 5.964 | 0.000 | 5.964 |
| F | 2.25 | 2.036 | 6.179 | 0.000 | 6.179 |
| M | 5.0 | 2.036 | 9.143 | 1.143 | 8.000 |
| A | 1.25 | 2.036 | 7.214 | 0.000 | 7.214 |
| M | 0.5 | 2.036 | 5.679 | 0.000 | 5.679 |
| J | 0.75 | 2.036 | 4.393 | 0.000 | 4.393 |
| J | 0.5 | 2.036 | 2.857 | 0.000 | 2.857 |
| A | 0.75 | 2.036 | 1.571 | 0.000 | 1.571 |
| S | 1.25 | 2.036 | 0.786 | 0.000 | 0.786 |
| O | 1.25 | 2.036 | -0.000 | 0.000 | -0.000 |
| N | 5.0 | 2.036 | 2.964 | 0.000 | 2.964 |
| D | 6.25 | 2.036 | 7.179 | 0.000 | 7.179 |

**(a)** Maximum uniform draw-off $=2.036\times10^6$ m³/month ($\approx0.77$ m³/s).

**(b)** Spillage $=1.143\times10^6$ m³ in the year (in March, when the reservoir is full).

**Answer: (i) draw-off = 2.396 Mm³/month, capacity = 10.52 Mm³, minimum initial storage = 6.46 Mm³. (ii) (a) draw-off = 2.036 Mm³/month; (b) spillage = 1.14 Mm³.**

## Check yourself

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

1. What is the maximum possible uniform draw-off over the driest year with unlimited storage?
   A. The minimum monthly flow, 0.5 Mm³
   B. The mean monthly inflow, 28.75/12 = 2.396 Mm³/month
   C. The maximum monthly flow, 6.25 Mm³
   D. Half the total annual flow
   Answer: B. Over the year you cannot draw more than the total inflow, so the maximum uniform draw-off is the mean, 2.396 Mm³ per month. (Key point: Maximum uniform draw-off)

2. How is the reservoir capacity obtained from the cumulative (inflow - draw-off) table?
   A. Highest cumulative value only (4.062)
   B. Lowest cumulative value only (6.458)
   C. Peak minus trough: 4.062 - (-6.458) = 10.52 Mm³
   D. Sum of all positive net values
   Answer: C. The capacity is the range between the highest and lowest points of the cumulative curve, which is 10.52 Mm³. (Key point: Capacity from mass curve)

3. What is the minimum initial storage on 1 January needed so that demand is never short?
   A. 6.46 Mm³, the depth of the lowest cumulative point (end of October)
   B. 4.06 Mm³, the peak in March
   C. 10.52 Mm³, the full capacity
   D. 2.40 Mm³, one month's draw-off
   Answer: A. The cumulative falls to -6.458 at the end of October, so 6.46 Mm³ must be in storage at the start to avoid shortage. (Key point: Minimum initial storage)

4. With a capacity of only 8 Mm³ (less than 10.52), what changes?
   A. Draw-off can be increased above 2.396
   B. Water spills when the reservoir is full, so the draw-off must be reduced (2.036 Mm³/month) and spill is 1.14 Mm³
   C. No water spills because the reservoir is small
   D. The initial storage is irrelevant and the draw-off stays 2.396
   Answer: B. A smaller reservoir spills in March when full, wasting water, so the maximum uniform draw-off falls to 2.036 Mm³/month with 1.143 Mm³ spilled. (Key point: Small reservoir: reduced draw-off and spill)

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