Irrigation Scheduling for a Dry Spell
A farmer grows cabbages on 0.4 hectares during a dry spell. The soil is a silt loam with a water-holding capacity of about 150 mm per metre of depth and an effective root depth of 30 cm. The crop's daily water use is about 5 mm per day. The available irrigation water is limited: the farmer has a 10,000-litre tank and a pump that delivers 5,000 litres per hour. The farmer can refill the tank once per day. Cabbage yield drops sharply if the crop uses more than 50% of the available soil water before irrigation. The farmer currently irrigates 20 mm every four days.
1. Calculate the total available water in the root zone and the allowable depletion before irrigation is needed. Then judge whether the current schedule of 20 mm every four days is adequate.
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Available water in the root zone = 150 mm/m × 0.30 m = 45 mm. The allowable depletion is 50% of this, so 22.5 mm. The crop uses 5 mm per day, so it reaches 22.5 mm of depletion in 22.5 ÷ 5 = 4.5 days. The current schedule applies 20 mm every 4 days. Over 4 days the crop uses 20 mm, so the 20 mm application replaces exactly the water used, and depletion never exceeds about 20 mm, which is below the 22.5 mm threshold. On paper the schedule is adequate, but it is tight: any hot day with higher water use, or a missed irrigation, would push depletion past the threshold. The judgement is that the schedule is acceptable but has little margin, so the farmer should monitor soil moisture and be ready to irrigate slightly earlier during hot weather.
2. Check whether the farmer's tank and pump can deliver the 20 mm application to 0.4 hectares. Show your calculations and state any constraint.
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Volume needed for 20 mm over 0.4 ha: 20 mm = 0.020 m. Area = 0.4 ha = 4,000 m². Volume = 0.020 × 4,000 = 80 m³ = 80,000 litres. The tank holds 10,000 litres, so the farmer needs 8 full tanks. The pump delivers 5,000 litres per hour, so one tank takes 2 hours to pump. Eight tanks would take 16 hours of pumping. The farmer can refill the tank once per day, meaning only 20,000 litres per day can be supplied if the tank is emptied and refilled once. To deliver 80,000 litres would take 4 days at that rate. This is a major constraint: the farmer cannot apply 20 mm to the whole plot in a single day. The judgement is that the irrigation schedule is limited by water supply, not just by crop demand, and the farmer may need to irrigate in sections or reduce the area planted.
3. Given the supply constraint, propose a practical irrigation plan that protects the cabbage crop and explain your reasoning.
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The farmer should divide the 0.4 ha plot into four sections of 0.1 ha each. Each section needs 0.020 m × 1,000 m² = 20 m³ = 20,000 litres for a 20 mm application. With a 10,000-litre tank refilled once per day, the farmer can supply 20,000 litres per day, which is exactly one section per day. Over four days the whole plot receives 20 mm, matching the original schedule. This works because each section is irrigated once every four days, and the crop's depletion stays near 20 mm, below the 22.5 mm threshold. The farmer should prioritise the most stressed section first and check soil moisture daily. If water use rises above 5 mm per day, the farmer may need to reduce the planted area or improve the tank capacity. The judgement is to match the irrigation layout to the available supply rather than assume the schedule is achievable.