Problem 270//Faucet finish

It’s the end of a long day, but Bernie Beaker has been given one last task by his boss, the venerable Professor Oltymer. The assigned task is to fill up a hundred 250-mL beakers with water to prepare for next morning’s science class. Once finished, he can head over to the annual Physics Department Fish Fry. Unfortunately, he only has 15 minutes before his wife Wanda is to pick him up for the event. He’s not sure if he can possibly do the job that quickly.

Bernie has the faucet open wide, and the cross sectional area near the mouth is 1.2 cm2. The stream of water narrows as it falls, and 45 mm lower, the cross section decreases to 0.35 cm2. At what rate is the water flowing, and how long it will take Bernie to fill up each 250 mL beaker? Will Wanda be waiting long? Assume surface tension is negligible – Bernie has enough to worry about!

Solution to problem 269, Grand math slam, June 2003:

Winners circle

Fun problem 268: Guzzlin’ grannies May 2003
Total entries: 64
Number correct: 8 (12.5%). The answer was 5.24 at 1.75; in the June issue, a typo in the solution reflected 1.05.
Winner: Derek Koonce
Derek’s prize: Inviting Disaster, Lessons from the Edge of Technology by James R. Chiles; Harper Business.
Combining riveting storytelling with eye-opening findings, Inviting Disaster shows what happens when our reach for new technology exceeds our grasp, and explains what we need to know to survive on the machine frontier.

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Fun With Fundamentals: Problem 269