Estimation question

How long would it take to empty a hot tub using only a drinking straw?

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What this question tests

Quick physical estimation using flow rate reasoning, checking whether you can build a simple model instead of guessing a number.

How to approach it

  1. Clarify assumptions: a standard hot tub holds roughly 1,500 liters, and a drinking straw has an inner diameter of about 5 millimeters.
  2. Model the straw as a siphon or suction tube, since gravity draw or manual suction determines flow rate, and assume manual suction at a comfortable sustained rate.
  3. Estimate flow rate through the straw: a person can realistically draw and expel roughly 20 to 30 milliliters per suction cycle, at about 1 cycle per second, so 20 to 30 mL per second if sustained, though real sustained rates are far lower due to fatigue.
  4. Adjust for a more realistic sustained rate, since no person could suction constantly for hours, so assume a mechanical or automated siphon drawing at a steady 10 mL per second instead.
  5. Compute time: 1,500 liters divided by 10 mL per second equals 150,000 seconds, roughly 41.7 hours.
  6. State the answer as an order of magnitude, roughly 1.5 to 2 days of continuous flow, and flag that human suction alone is impractical, so a passive siphon assumption is more realistic.

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