A lazy day

Classical Mechanics Level 5

As I was reclining on my couch on a beautiful fall day, I watched the breeze blow through my window fan, thereby making the blades spin. Of course, I immediately thought - nice Brilliant problem! So here it is. My window fan opening is circular with a radius of 0.1 m. If air blows into this opening with a speed of 1 m/s and exits with a speed of 0.9 m/s, how much power is delivered to the blades of my window fan in Watts? You may take the density of air to be \(1.22~\text{kg/m}^3\).

Assumptions and Details

  • Assume that 10% of the air flowing into the fan fan scatters radially (with respect to the center of the fan) away from the window, so as not to contribute to the mass flow through the fan.
Image credit: Wikipedia Nuberger13

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