An irrigation command area has a base period of $B = 120.0\text{ days}$ for wheat cultivation. The duty of irrigation water at the field head is $D = 1440.0\text{ ha/cumec}$. The total depth of irrigation water (delta, $\Delta$) required by the crop over the base period in centimeters ($\text{cm}$) is ________ (round off to one decimal place).
Answer Key:
72.0
Step-by-Step Solution & Explanation
1. Relationship between Duty ($D$), Delta ($\Delta$), and Base period ($B$):
$\Delta = \frac{8.64 \cdot B}{D}$
Where:
- $\Delta$ is in meters
- $B$ is in days ($120.0\text{ days}$)
- $D$ is in $\text{ha/cumec}$ ($1440.0\text{ ha/cumec}$)
2. Calculating $\Delta$:
$\Delta = \frac{8.64 \times 120.0}{1440.0} = \frac{1036.8}{1440.0} = 0.720\text{ m}$
3. Converting to centimeters:
$\Delta = 0.720 \times 100 = 72.0\text{ cm}$