The duty of canal water (hectare per cm per second) 'D', base period of crop 'b' in days and delta 'd' in meter are related as:
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The relationship \( \Delta = \frac{8.64 B}{D} \) (with \(\Delta\) in meters, B in days, D in ha/cumec) is one of the most fundamental formulas in irrigation engineering. Always be careful with the units, as they determine the constant (e.g., it becomes 864 if Delta is in cm).
Step 1: Define the terms Duty (D), Base Period (b), and Delta (d). - Duty (D): Land area (hectares) irrigable by 1 cubic meter per second (cumec) of water flowing continuously for the entire base period. - Base Period (b): Total days irrigation is supplied to a crop. - Delta (d): Total depth of water (meters) required by a crop during the entire base period. Step 2: Derive the relationship. Consider a discharge of 1 cumec over 'b' days. Total water volume, V = Discharge \(\times\) Time \[ V = (1 \text{ m}^3/\text{s}) \times (b \text{ days}) = 1 \times (b \times 24 \times 60 \times 60) \text{ m}^3 = 86400 \cdot b \text{ m}^3 \]This volume irrigates 'D' hectares to a depth of 'd' meters. Volume used on land = Area \(\times\) Depth \[ V = (D \text{ hectares}) \times (d \text{ meters}) = (D \times 10^4 \text{ m}^2) \times (d \text{ m}) = 10000 \cdot D \cdot d \text{ m}^3 \]Equating the volumes: \[ 10000 \cdot D \cdot d = 86400 \cdot b \]\[ D = \frac{86400}{10000} \frac{b}{d} = 8.64 \frac{b}{d} \]