Duty and minor discharge, wheat 400 ha

Given: area = 400 ha (all wheat), kor period $B = 3$ weeks = 21 days, kor depth = 10 cm, rainfall = 2.75 cm of which 50% is surface runoff (not useful), conveyance loss = 10%.

Effective rainfall

$$P_e = 0.5\times 2.75 = 1.375\ \text{cm}$$

Net kor depth to be supplied by irrigation

$$\Delta = 10 - 1.375 = 8.625\ \text{cm} = 0.08625\ \text{m}$$

(a) Duty at the field head

$$D_{field} = \frac{8.64\,B}{\Delta} = \frac{8.64\times 21}{0.08625} = 2103.7\ \text{ha/cumec}$$

(b) Discharge of the minor at the upstream head

$$Q_{field} = \frac{400}{2103.7} = 0.1901\ \text{cumec}$$

Allowing 10% conveyance loss:

$$Q_{head} = \frac{0.1901}{1-0.10} = 0.2113\ \text{cumec}\ (211\ \text{l/s})$$

(The duty at the head of the minor is $D_{field}\times0.9 = 1893.3$ ha/cumec.)

Answer: (a) duty at field head $\approx$ 2104 ha/cumec; (b) discharge at the head of the minor $\approx$ 0.211 cumec.