Question

An anemometer is mounted at the hub of the nacelle at a height of 40 meters above the ground surface. A wind speed of 9 m/s is indicated by the last observed measurement. Assume the pressure at 40 m is 1 atm and the temperature is 20 The Hellman exponent is known to be 0.1. a) Evaluate the air density at 40 m under the conditions given above.

Answer 1

Given height - uom dir pressurez larm = 101325 pascal wind speed = 9m/s Temp= 20°c = (273.156 + 20 ) K = 293.15k for calculating air density Ideal gas law ie. PV = nRT or PVz mRI where pa air presgure (Pa) Ve volume (m3) m a mass of air (kg) Ragas constant (J/kg .K) = 287005 J/kg .k To Temp (K) Density of air po m e . P for Pz lahm, T= 20°c is R1

Pa 101325 287.05X (293115) z lo2oul k 1. b) wind power dersity is given an air density of the site x wind speed) WPD: { x 1.2041X(9) 3 =438.90 watt per square meter

O for a height of 23om, - Bince at 40m height, prenure is assumed to be lahm ar 181325Pa, we can asume that tom is mean sear level therefore for hz 230m -0.00012 (230-40) P(n) 101.325e 2990040 kla i Pzxom, zo? 99040 287.05% 293.15 - 1.1769 kg/m3 with height , velocity all changes, Violino ( 730m) > Uusind tromi Xh2go) where of Hell mom constant . I huo ... wind velocity at 230 m 29 x 230 = 10.720ms

o wind tower density at 230m at 20°c is Wro - 1 x wind domity X (wind speed)3 wlm- 2 1/2 x 1.1769 X (10.72}} 2 724.99 Wall / m2 (d) for a height of 170m at 0°c air prenure P(170) > 101325e -0.000121170-48). 599756.59 Pa air density z P 1 RT 299756.59 ,as T2 273.15eu 27805X273:15 273-)5k 21-313 kg km3

wind speed at 170m = 9x (470) C) 2 10.401 mis .. wind power density at 170m and 0°c * *1.313 x 10.401) 2738.71 watt/m²