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Impounded reservoir, 9688 million L per month

Short answer

Annual river inflow (68.93 million m³) is much smaller than annual demand (116.26 million m³). No impounded reservoir can meet this demand; the given data cannot sustain the required draft.

The city has an average water demand of 9688 million liters per month. Calculate the capacity of the impounded reservoir. The flow in the river is shown below.

MonthInflow (m3^3/s)
January2.51
February2.11
March1.20
April0.00
May0.11
June1.00
July1.30
August3.00
September4.00
October5.2 [?]
November4.00
December1.80

A reservoir can only store water that the river actually brings in. The solution uses the mass curve (analytical) method, with volumes in million m3^3 (1 ML = 1000 m3^3, V=Q×86400×V = Q\times86400\times days).

Demand D=9688 ML/month=9.688 Mm3D = 9688\ \text{ML/month} = 9.688\ \text{Mm}^3/month. The October flow in the given data is doubtful (shown as 5.2 m3^3/s); it has been used as given.

MonthInflow (Mm3)Demand (Mm3)Surplus/deficitCumulative
Jan6.7239.688-2.965-2.965
Feb5.1059.688-4.583-7.549
Mar3.2149.688-6.474-14.023
Apr0.0009.688-9.688-23.711
May0.2959.688-9.393-33.104
Jun2.5929.688-7.096-40.200
Jul3.4829.688-6.206-46.406
Aug8.0359.688-1.653-48.059
Sep10.3689.688+0.680-47.379
Oct13.9289.688+4.240-43.139
Nov10.3689.688+0.680-42.459
Dec4.8219.688-4.867-47.326

The total inflow in the year is 68.9368.93 Mm3^3, while the total demand is 12×9.688=116.2612\times9.688 = 116.26 Mm3^3. The yearly inflow is much less than the demand, so the cumulative balance keeps falling and reaches -47.33 Mm3^3 at the end of the year.

Answer: With the data as printed, no impounded reservoir can meet this demand, since the annual inflow (68.93 Mm3^3) is smaller than the annual demand (116.26 Mm3^3). The largest average draft the river can sustain is 5.744 Mm3^3/month; for a demand at or below this value, the same table method gives the storage as the largest cumulative deficit. The demand figure (or the table) appears to be misprinted.

✓ Answer checked by Claude Opus 5.5 (high effort)

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