Question 13.SQ.6: Continue Example 13.10 by assuming that the reservoir is sti......
Continue Example 13.10 by assuming that the reservoir is still full initially, but the maximum reservoir storage is now limited to 15.00 × 10^6 m³. (a) What is the maximum uniform demand that can be maintained throughout the year, and (b) how much water will discharge over the spillway?
The cumulative inflow, ΣI, is as in Example 13.10, and is shown below and plotted in Fig. 13.19.
(a) With the maximum storage capacity limited to 15.00 × 10^{6} m³, the graph must be replotted so that AB = 15.00 × 10^{6} m³, as in Fig. STQ13.6. The new uniform demand that can be supported is given by a line passing through 0 and B, which can be extrapolated to C. At C it has a value of about 55.90 × 10^{6} m³. Thus the gross uniform monthly demand that can be supported is 55.90 \times 10^6 / 12 = 4.66 \times 10^6 m ^3, which becomes (4.66 – 0.81) = 3.85 × 10^{6} m³ with the compensation flow deducted. (Numerical check: B has a value of (12.96 + 15.00) = 27.96 × 10^{6} m³, so the gross yield is 27.96 \times 10^6 m ^3 / 6=4.66 \times 10^6 m ^3, as above.)(b) The reservoir is initially full, and is full again when the demand line ΣO and ΣI lines cross in December. From December to the end of March the inflow exceeds the demand so the surplus inflow is passing over the spillway. The cumulative volume discharged over the spillway at the end of March is given by the ordinate CD in Fig. STQ13.6, which is about 19.20 × 10^{6} m³. (Numerical check: from above the total demand at C is 55.90 × 10^{6} m³ and ΣI at D = 75.10 × 10^{6} m³, so the difference CD is 19.20 × 10^{6} m³.)
