Question

The gross commanded area for a distributary is 12000 hectares, culturable command area in Kharif and Rabi season is 3554.4 hectares, and 2369.9 hectares, respectively. If the average duty at the head of the distributary is 2150 hectare per cumec for rabi season and 1900 hectare per cumec for kharif season, then determine the discharge required at the head of the distributary from average demand consideration (nearest to closest value)

1. 1.49 cumecs
2. 1.10 cumecs
3. 1.29 cumecs
4. 1.25 cumecs

Answer 1

Correct Answer - Option 1 : 1.49 cumecs

Explanation:

For Kharif: 

The culturable command area = 3554.4 hectares

Duty at the head of the canal = 1900 hectare per cumec

Discharge required(Q₁) = \(\frac{{{\rm{Culturable \ command\ area}}}}{{{\rm{Duty}}}}\)

Discharge required(Q1) = \(\frac{{{\rm{3554.4}}}}{{{\rm{1900}}}}\)

Discharge required(Q1) = 1.87 cumec

For Rabi: 

The culturable command area = 2369.9 hectares

Duty at the head of the canal = 2150 hectare per cumec

Discharge required(Q2) = \(\frac{{{\rm{Culturable \ command\ area}}}}{{{\rm{Duty}}}}\)

Discharge required(Q2) = \(\frac{{{\rm{2369.9}}}}{{{\rm{2150}}}}\)

Discharge required(Q2) = 1.10 cumec

Average discharge required(Q_av):

\({{\rm{Q}}_{{\rm{av}}}} = \frac{{{{\rm{Q}}_1} + {{\rm{Q}}_2}}}{2}\)

\(​​{{\rm{Q}}_{{\rm{av}}}} = \frac{{{{\rm{1.87}}\ } + {{\rm{\ 1.10}}}}}{2}\)

Q_av = 1.485 cumec = 1.49 cumec.