Uniform draw-off and reservoir capacity

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):

• 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):

(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.