Analyzing air resistance and energy expenditure to conclude the optimal fan design.

Question: Nityaansh, Abid, and Rishabh were in the bus going back home on a hot, summer day. They started talking about efficient cooling solutions for a room with just a ceiling fan. Rishabh suggested a four-blade ceiling fan arguing that having an extra blade would reduce the power consumption by one blade, increasing the efficiency of the fan. Nityaansh suggested a regular three-blade fan with longer blades saying that the work done to reach the same angular velocity would be lesser. Abid, after carefully considering both the fan designs suggested a third kind of fan – a three-blade ceiling fan that had curved blades so that the design was more aerodynamic. The fans and their dimensions are given below.

Some calculations might be necessary to show which fan design will be more efficient.

Comment on each design. Which general design do you agree with, and why?

My answer: