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# Physics: Energy conservation

Read carefully the Reference section and the Competition Rules for the Wind Turbine Project and answer the following.

1. The 20-inch box fan used in Project 1 consumes about 85 watts of electricity (on high setting) and delivers a useful stream of air moving with the maximum velocity of about 15 feet per second.  Estimate the mechanical power of wind (or the kinetic power of the moving air) from equation 321windwindAVP (in watts).   Assume that the fan generates a ‘tube’ of wind 20 inches in diameter and with uniform wind speed of 15 ft/s.  What is the efficiency of the power conversion in the fan (in percent)?    Convert all non-SI units to SI units.

2. In real wind turbines mechanical power of wind Pwind is first converted to shaft power of the turbine rotor Protor, then the a gear box converts it to shaft power of an electric generator Pgenerator , finally the generator converts it into electric power Pelectric.  If the efficiency of the three power conversion steps are %30blades, %88gearbox and %95generator, respectively, what is the overall power conversion efficiency of the whole wind turbine?   Draw a block schematic showing the flow of power into and out of each power conversion stage.

3. If an 18-inch diameter turbine rotor spins at 90 revolutions per minute (or rpm), and the wind speed is 15 ft/s, what is the resulting tip speed ratio windtipVV/?    Perform your calculations in US Customary units (do not convert to SI).    Examining the Reference section, what levels of power coefficient CP can you expect from the turbine you are building in the Wind Turbine Project?  Note that the power coefficient CP is synonymous with  blades discussed in Problem 2.

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