# HW4_solutions - ECE 333 Homework 4 Solutions Spring 2010 1...

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ECE 333 Homework 4 Solutions :: Spring 2010 1 A horizontal-axis wind turbine with rotor 20 meters in diameter is 30-percent efficient in 10 m/s winds at 1 atmosphere of pressure and 15 o C temperature. a. How much power would it produce in those winds? P !"# P wind !"# 1 2 \$ A v 3 ! 0.3 " 1 2 1.225 # 4 20 2 10 3 ! P \$ 57.73 kW b. Estimate the air density on a 2500-meter mountaintop at 10 o C. From Table 6.1 the density at 10 o C is 1.247 kg/m 3 , yielding a K T ratio of 1.247/1.225 = 1.018. Using (6.13), the density ratio, K A , can be found: P ! P 0 exp !" 1.185x10 " 4 # 2500 \$% 0.9109 & K A ! 0.9109 1.225 ! 0.743 The air density at 2500-meters can now be found using (6.14): "! 1.225 K T K A ! 1.225 " 1.018 " 0.743 #\$! 0.927 kg % m 3 Note that (6.7) could also be used to find the same solution. c. Estimate the power the turbine would produce on that mountain with the same windspeed assuming its efficiency is not affected by air density. Turbine power is proportional to air density therefore: P ! 57.73 kW ! 0.927 1.225 " P # 43.7 kW 2 An anemometer mounted 10 m above a surface with crops, hedges and shrubs, shows a windspeed of 5 m/s.

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