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2. (a) In a location with a wind-speed probability distribution f(u), and a value of the power coefficient Cp that also varies as a function of the wind-speed, show that the average power output from a wind-turbine is given by: 1 Po = pa ſº call_u’rluydu. SpA [2] The integral is approximately equal to 0.35 (u), where (u) is the wind speed at the height of the turbine hub. In this case the average power can be written as: Po ~ KDP (u)3, where D is the diameter of the turbine. Find the value of K, assuming p = 1.2 kg m-3. [2] Assume that in a windfarm there is a further loss factor equal to 0.9. If the spacing between the turbines is 8D (downwind) and 5D (crosswind), give an expression for the average output per unit land area (Parea). Express your units in MW km-2. [2] Evaluate Parea for a location in which (u) = 8.5 ms-1. = [2]