Concept:
\({\rm{Discharge}} = \frac{{{\rm{Area}}}}{{{\rm{Duty}}}}\)
Calculation:
Given:
Culturable command area (CCA) = 50,000 ha
Intensity of irrigation for the kharif season = 50%
Culturable cultivatable command area (CCCAk) = 0.5 × 50000 = 25000 ha
Duty of kharif season = 1000 hectares/cumec
\({\rm{Discharge}} = \frac{{{\rm{Area}}}}{{{\rm{Duty}}}}\)
Transmission loss = 10%
∴ η = (100 - 10) = 90%
Discharger at head of canal = 25/0.9 = 27.78 cumec
∴ The required discharge (in cumec) at the head of the canal is 27.78