The Failing Water Tank Sensor
A community water tank holds 10,000 litres and is refilled by a pump at 500 litres per hour. A sensor triggers the pump when the level drops to 4,000 litres and stops it at 9,500 litres. Households draw water at a steady 700 litres per hour during the day. Last week the tank ran dry twice, even though the pump was working and the sensor readings looked normal. A technician found that the sensor reads 300 litres higher than the true level once the tank is below half. The community has 200 households and no backup supply. Repairing the sensor takes two days and costs 800 currency units.
1. Using the numbers, explain why the tank ran dry despite a working pump.
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True trigger point: the sensor reads 300 L high below half, so it starts the pump when it thinks the level is 4,000 but the true level is 4,000 − 300 = 3,700 L.
Draw vs refill: households draw 700 L/h, pump adds 500 L/h, so net loss while pumping = 200 L/h. The tank keeps falling even with the pump on.
Time to empty from 3,700 L: at net 200 L/h, that is 3,700 ÷ 200 = 18.5 hours to reach zero if demand continues. If the pump only starts at 3,700 and demand is continuous, the tank can empty before the sensor ever reads the stop level.
So the pump is not the problem: the refill rate (500) is below the draw rate (700). The sensor error just delays the start and hides the shortfall. The dry-outs are a capacity/rate mismatch, exposed by a sensor fault.
2. The technician says fixing the sensor will solve the problem. Evaluate this claim.
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The claim is only partly right. Fixing the sensor makes the pump start 300 L earlier (at true 4,000 instead of 3,700), which buys roughly 300 ÷ 200 = 1.5 hours of buffer. That is marginal.
The core arithmetic is unchanged: 500 L/h in, 700 L/h out, net −200 L/h whenever the pump runs. No sensor setting can make a 500 L/h pump keep up with 700 L/h demand over a full day.
So the sensor repair (800 units, two days) is necessary for accurate readings but not sufficient. A correct judgement separates the measurement fault from the throughput fault. Fixing the gauge on a leaking bucket does not stop the leak.
3. Recommend a plan the community can act on within the two-day repair window, given no backup supply.
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Immediate (during repair): demand reduction is the only lever that closes a 200 L/h gap without new supply. Cutting draw by about 30% (700 → 490 L/h) makes net positive (500 − 490 = +10 L/h). Practical steps: restrict daytime draw to fixed hours, prioritise drinking and cooking, pause non-essential uses (gardening, washing vehicles).
Short term: stagger household draw so the pump is not chasing simultaneous demand; verify the true level manually (dipstick) while the sensor is unreliable, since the sensor over-reads by 300 L below half.
Medium term: the numbers show a structural deficit of 200 L/h at peak. Options: add a second pump or a larger pump (raise inflow above 700), or add storage so refills happen overnight when draw is low. Storage is often cheaper than pumping capacity.
Judgement: sequence by urgency. Stop the dry-outs first with demand management, then fix the sensor for accuracy, then address the 500-vs-700 mismatch permanently. Do not present the sensor repair as the solution.