Mass curve and critical period storage

Units are m³/s-months; one m³/s-month $=2.628\times10^6$ m³.

i) Mass curve

Mean inflow $=\dfrac{\sum Q}{12} = \dfrac{179}{12} = 14.917$ m³/s, taken as the uniform draft.

 Cum.
 volume
  179 |                          ____*   inflow mass curve
      |                   ___---
      |              _--*      draft line (slope = mean)
      |        __.-*      .-'
      |   _.-*      _.--'
      | *     _.--'
      +---------------------------
       Oct                    Sep

The mass curve of inflow lies above the draft line from October to February (surplus) and below it from March to September (deficit, the reservoir is drawn down).

ii) Storage capacity and critical period

The largest vertical gap between the draft line (tangent to the mass curve at the end of February) and the mass curve is at the end of September. This is the sum of the deficits from March to September:

$$S = \sum(\bar Q - Q)_{Mar-Sep} = (4.917+6.917+7.917+8.917+10.917+11.917+11.917) = 63.42\ \text{m}^3/\text{s-months}$$ $$S = 63.42\times2.628\times10^6 = 166.7\times10^6\ \text{m}^3$$

Critical period $=7$ months (March to September), when the reservoir goes from full to empty. It refills by about February of the next year.

iii) Draft = 80% of mean inflow

$0.8\times14.917 = 11.933$ m³/s. Deficit months are those with inflow below this value (Mar to Sep: 10, 8, 7, 6, 4, 3, 3):

$$S_{80} = (1.933+3.933+4.933+5.933+7.933+8.933+8.933) = 42.53\ \text{m}^3/\text{s-months} = 111.8\times10^6\ \text{m}^3$$

The critical period is still March to September (7 months). The storage required is reduced from 166.7 Mm³ to 111.8 Mm³, a saving of 33%, but the water supplied also falls by 20%.

Answer: storage for the mean-flow draft = 166.7 Mm³ (63.42 m³/s-months), critical period = 7 months; storage for 80% draft = 111.8 Mm³ (42.53 m³/s-months).