Question 13.9: The figures below show the riverflow in units of 10^6 m³ at ......
The figures below show the riverflow in units of 10^6 m³ at a potential reservoir site during a drought year. To be viable, the reservoir must provide at least 5.00 × 10^{6} m³ per month throughout the year. A constant compensation flow of 0.81 × 10^{6} m³ per month must pass through the dam (including the months when flow passes over the spillway). Assume that the reservoir is initially full, that it must refill by the following April, and that all months are of equal length. Using a tabular method, determine (a) whether or not the reservoir could sustain the demand during this drought year; (b) the volume of storage required; (c) whether any flow passes over the dam’s spillway.
The total demand per month = (5.00 + 0.81) × 10^{6} = 5.81 \times 10^{6} m³. Assume that this is an average value that can be considered constant throughout the year. The calculations are shown in Table 13.13. They proceed month by month with the change in storage S = Inflow – Outflow.
| Table 13.13 Inflow, outflow and storage calculations for Example 13.9 | ||||
| Month | Inflow
(10^{6} m³) |
Outflow
(10^{6} m³) |
Change in storage, S
(10^{6} m³) |
ΣS
(10^{6} m³)
|
| Apr | 3.15 | 5.81 | – 2.66 | – 2.66 |
| May | 2.53 | 5.81 | – 3.28 | – 5.94 |
| Jun | 2.05 | 5.81 | – 3.76 | – 9.70 |
| Jul | 1.88 | 5.81 | – 3.93 | – 13.63 |
| Aug | 1.50 | 5.81 | – 4.31 | – 17.94 |
| Sep | 1.85 | 5.81 | – 3.96 | – 21.90 |
| Oct | 8.70 | 5.81 | + 2.89 | – 19.01 |
| Nov | 9.13 | 5.81 | + 3.32 | – 15.69 |
| Dec | 13.85 | 5.81 | + 8.04 | – 7.65 |
| Jan | 12.65 | 5.81 | + 6.84 | – 0.81 |
| Feb | 10.98 | 5.81 | + 5.17 | + 4.36 |
| Mar | 6.83 | 5.81 | + 1.02 | + 5.38 |
(a) The yield can be sustained during the dought year since the total storage change over the 12 month period is + 5.38 × 10^{6} m³, indicating that inflow exceeds outflow by this amount.
(b) The volume of storage required is 21.90 × 10^{6} m³.
(c) Since the reservoir is full initially, the surplus inflow (5.38 × 10^{6} m³) discharges over the spillway.