Activity 1 (5 points): Energy Transfers and Transformations in Windmills Wind energy is the kinetic energy of the moving air. For a mass m of air moving with a speed v, the kinetic energy can be calculated using the usual formula: K = 1/2 mu2 Since we have a fluid (air) of some volume, V, and density, p, that is flowing, we can rewrite the kinetic energy equation as K = 1/2 va2 The input wind power, PW, is the rate at which this kinetic energy is fed into the windmill. The wind power is given as Pw21/219AV3 V Where v is the wind velocity, A is the crosssectional area of the blades and p is the density of air at sea level. Thus, the wind power increases with the cube ofthe wind speed, and depends on the crosssectional area swept by the blades as they rotate. Let's calculate the power generated by the simple windmill that Kamkwamba built in his village. Follow the steps below to complete the calculation: I: Write down values for the terms in the equation for the power, PW. Use SI units throughout. a. Look up the density of air at sea level. 9 : b. Later in the book {on page 185 in Chapter 11), Kamkwamba describes the first big windmill he and his friends built. He notes that the \"wingspan of the blade system was more than eightfeet across". Convert this value to SI units. Using this value as the diameter of the circle swept by the blades (as shown in the figure above), calculate the area A. Diameter in meters, :1 = Radius in meters, 1" = Area A = RT2 = c. The graph below shows wind speeds in Lilongwe, Malawi year-round. Using the month of your birth, note down the value of the average wind speed (shown by the dark gray line}. Don'tforget to convert the speed to Si units! Average Wind Speed windy 16 mph 16 mph 14 mph 14 mph 12 mph 12 mph 10 mph 10 mph 3 mph 6 mph 5 mph Rm 6 mph 4 mph 4 mph 2 mph 2 ITIIJl'I 0 mph 0 mph Jan Feb Mar Apr May Jun Jul Aug Sop Oct Nov Den The average of mean noun-'3! wind speeds .'Gork gray lice}. with Bid? to F50? and Tori: to SOL"? per'renriie bonds. d. Complete the calculation of the wind power, in Watts. e. The efficiency of wind turbines in converting wind power to electrical power ranges from about 10% - 40%. Using an efficiency of 20%, calculate the electrical power output of Kamkwamba's windmill (in Watts) Output power, P9 = 20% PW = f. To finish off, on page 208, Kamkwamba writes that he powered his bedroom with the light from a small car bulb (typically, the interior dome bulb in cars}. These bulbs require about SW of power. Was his windmill able to power such a lightbulb, according to your calculations? YES NO