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Optimized Blade Design for Homemade Windmills

224 bytes added, 03:42, 16 April 2010
Power Available to the Turbine
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Area of The kinetic energy stored in the cylinder base is calculated bywind can be found according to Bournoulli's equation:
A <math> KE = 1/4 2 (π m * Dv^2) </math>
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Length of the cylinder is based on the velocity of wind multiplied by time:
L = v * t In order to find the energy in the wind, we must find the mass of the cylinder. This is based on the volume of the cylinder multiplied by the density of the fluid:
<brmath> m = \pi * V </math>
Combining these values, we are able to compute the total volume of the fluid cylinder:
V = A * L
<br> The total volume of the fluid that is represented by cylindrical column is:
The mass of the cylinder is based on the density of the fluid multiplied by the volume: <math> V = A * L </math>
m = ρ * V
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The Kinetic Energy We can then be found by multiplying calculate the mass area of the fluid cylinder's base by :  <math>A = 1/4 (\pi * D^2) </math>   The length of the half cylinder represents the amount of fluid that has passed through the windmill's swept area. This is calculated by multiplying the velocity squaredof wind by time:  <math> L = v * t </math>
KE = 1/2 (m * v^2)
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This can be simplified as follows:
<math> KE = 1/8 (ρ \rho * π \pi * D^2) * v^3 * t <br/math>  
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Finally, the power in the wind is simply the energy per unit of time
<math> P = π\pi /8 (ρ \rho * D^2 * v^3) </math>
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As demonstrated, the power in the wind highly related to the velocity of the wind and to a lesser extent, the diameter of the turbine blades
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=== <br>'''Maximum Possible Efficiency''' ===
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