WindSolns - 1 ME 417 Design of Alternative Energy Systems...

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Unformatted text preview: 1 ME 417 Design of Alternative Energy Systems Wind Energy Problems Solutions 1. A downtown city terrain is under consideration for a wind farm. At 15 meters the wind velocity is found to be 4.3 m/s. Develop a graph of wind power density versus height for this locale. Solution: By definition we have 3 v 2 1 A W w r & & ρ = = ′ ′ Hence to graph the wind power density against height, we need to determine the velocity at different heights. Recall that we have the relationship n 1 2 1 2 h h v v = r r where for a downtown city terrain we have n = 0.4. Then we could write 4 . 15 h ) 3 . 4 ( v = r For the air density we will use the ideal gas law RT P = ρ We will assume that we are at standard conditions, so that kg/m 1.18 (298) (8.314/29) 101 3 = = ρ So we can now go to Excel and make the following table h (m) v r (m/s) w ′ ′ & (W/m 2 ) 10 3.66 28.89 15 4.30 47.00 20 4.82 66.37 25 5.27 86.75 30 5.67 107.97 35 6.03 129.91 40 6.37 6....
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WindSolns - 1 ME 417 Design of Alternative Energy Systems...

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