To find the capacity of the reservoir, we use the concept of Delta, which is the total depth of water required by a crop for its entire growing period. The steps are outlined below:

1. Key Formula:

$\Delta = \frac{8.64 \cdot B}{D}$ where:

• $\Delta$ = Delta in meters (depth of water required for the crop)
• $B$ = Base period in days
• $D$ = Duty in hectares/cumec

2. Net Water Requirement:

The Net Water Requirement ($NWR$) for each crop is: $NWR = \Delta \cdot \text{Culturable Command Area (CCA)} \cdot \frac{\text{Irrigation Intensity}}{100}$

3. Total Water Requirement:

The Total Water Requirement accounts for canal and reservoir losses: $TWR = NWR \cdot (1 + \text{Canal Loss Fraction}) \cdot (1 + \text{Reservoir Loss Fraction})$

4. Calculate for Each Crop:

a. Rice:

$\Delta_{\text{Rice}} = \frac{8.64 \cdot 120}{1800} = 0.576 \, \text{m}$ $NWR_{\text{Rice}} = 0.576 \cdot 80000 \cdot \frac{25}{100} = 11520 \, \text{hectare-meters}$

b. Wheat:

$\Delta_{\text{Wheat}} = \frac{8.64 \cdot 120}{2000} = 0.5184 \, \text{m}$ $NWR_{\text{Wheat}} = 0.5184 \cdot 80000 \cdot \frac{30}{100} = 12441.6 \, \text{hectare-meters}$

c. Sugarcane:

$\Delta_{\text{Sugarcane}} = \frac{8.64 \cdot 320}{2500} = 1.10592 \, \text{m}$ $NWR_{\text{Sugarcane}} = 1.10592 \cdot 80000 \cdot \frac{20}{100} = 17694.72 \, \text{hectare-meters}$

5. Add Total Net Water Requirement:

$\text{Total NWR} = 11520 + 12441.6 + 17694.72 = 41656.32 \, \text{hectare-meters}$

6. Apply Losses to Find Total Water Requirement:

$\text{Canal Loss Fraction} = 5\% = 0.05, \quad \text{Reservoir Loss Fraction} = 10\% = 0.10$ $TWR = 41656.32 \cdot (1 + 0.05) \cdot (1 + 0.10) = 41656.32 \cdot 1.05 \cdot 1.10 = 48157.42 \, \text{hectare-meters}$

7. Convert to Cubic Meters:

1 hectare-meter = $10^4 \, \text{m}^3$ $\text{TWR in cubic meters} = 48157.42 \cdot 10^4 = 481574200 \, \text{m}^3$

Final Answer:

The capacity of the reservoir is approximately 481.57 million cubic meters (MCM).

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Do you want detailed calculations or clarifications?

Related Questions:

1. How is the duty of water affected by soil type or crop variety?
2. What are the assumptions behind irrigation intensity calculations?
3. How can the reservoir losses be minimized in real-world applications?
4. What is the impact of climate change on irrigation and water management systems?
5. Why is it essential to include losses in reservoir capacity calculations?

Tip:

Always consider local climatic and soil conditions while estimating crop water requirements to avoid over- or under-designing reservoirs.