Sizing a Solar Pump and Fixing Brown Water at a School
A government middle school has 300 students and 12 staff and needs about 4,000 litres a day for drinking, handwashing and the mid-day meal. Water is lifted from a dug well by a submersible pump against a total head of 25 m, including friction losses, at a pump efficiency of 45%. The school plans a stand-alone solar array of 250 Wp modules, with 5.2 peak sun hours in the driest month and a 20% derating for dust, wiring and temperature losses. The overhead tank holds 5,000 litres. Separately, the caretaker doses the tank with bleaching powder, and after every dose the water at the taps turns brown and stains the whitewashed walls; two teachers want the tank 'cleaned' with a stronger dose. The well yields about 6,000 litres a day in most months but falls to 3,000 litres in May. The school roof area is 250 m² and annual rainfall is 1,100 mm.
1. Calculate the daily electrical energy required and the minimum number of 250 Wp modules. State a practical recommendation with a margin and justify it.
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Hydraulic energy. E = mgh = 4,000 kg × 9.81 m/s² × 25 m = 9,81,000 J = 0.2725 kWh per day.
Electrical energy drawn by the pump. 0.2725 ÷ 0.45 = 0.606 kWh/day.
Output of one module. 0.25 kW × 5.2 h × 0.8 = 1.04 kWh/day.
Modules. 0.606 ÷ 1.04 = 0.58, so one module meets the average day arithmetically.
Recommendation: install two modules. One module has no margin for the three things the calculation hides - dust and soiling, the water level falling in May (which raises the actual head above 25 m), and cloudy days when the pump must still fill a 5,000-litre tank. Two modules give roughly 1.7 times the requirement, so the tank can also be filled on a bad day and the school can shift pumping to the morning without running the pump dry. The pump should be a direct-drive unit with dry-run protection, and the array should be mounted at a tilt that sheds dust.
2. Explain why the water turns brown after bleaching powder is added, and prescribe the correct treatment sequence and chlorine residual target.
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The symptom points to iron in the well water, not to a poisoned tank.
What happens. Iron is present as soluble ferrous iron (Fe²⁺). Chlorine oxidises it to ferric iron (Fe³⁺), which forms insoluble rust particles - hence the brown colour and the stains on whitewash. Two consequences follow: the iron consumes chlorine, so no protective residual is left, and the turbidity physically shields bacteria from disinfection. Adding a stronger dose makes the staining worse and wastes chlorine.
Correct sequence.
- Test iron, turbidity and pH before treating.
- Aerate the water (spray or cascade into a settling tank) so iron oxidises and settles.
- Filter through sand or a multimedia filter to remove the particles.
- Chlorinate after clarification, to a free residual of about 0.2–0.5 mg/L at the tap.
- Store covered and test residual weekly.
If bacteriological contamination is also suspected, do not rely on chlorine alone until the water is clarified; boil drinking water in the interim and tell the staff that the brown colour is an aesthetic and treatment problem, not evidence of poison.
3. In May the pump runs dry and the school still demands 4,000 litres a day. Diagnose the failure and give engineering plus operational fixes, quantifying what rooftop harvesting can contribute.
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Diagnosis. The static water level falls in May, so the pump intake is exposed and the direct-drive pump keeps running because it has no dry-run cut-off. The demand stays constant at 4,000 litres while the well yields only 3,000 litres, so the shortfall is 1,000 litres a day - a supply problem, not a pump fault.
Engineering fixes. Lower the intake or fit a submersible pump that can sit deeper; add a float switch or dry-run protection that cuts the pump when the level drops; install a level controller on the overhead tank so the pump stops when it is full.
Operational fixes. Pump only in the cool morning hours, stagger washing and the mid-day meal so the peak draw is lower, and use handwash water for the school garden.
Rooftop harvesting. Volume = 250 m² × 1.1 m × 0.8 runoff coefficient = 220 m³ = 2,20,000 litres a year, roughly 600 litres a day averaged over the year - but concentrated in the monsoon, so it must be stored. A 10,000-litre tank covers about ten May days at the 1,000-litre shortfall, which is worth building only alongside recharge of the well itself.