A site's wind speed follows a Weibull distribution with shape parameter and scale…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Energy resources and conversion

Energy from Physics, Ch Natural energy flows: rotors, turbines, waves, channels and hot rock

Problem

A site's wind speed follows a Weibull distribution with shape parameter kW=2.5k_{\rm W} = 2.5 and scale parameter cW=7 m s−1c_{\rm W} = 7\,\mathrm{m\,s^{-1}}. Using ⟨vn⟩=cWnΓ(1+n/kW)\langle v^n\rangle = c_{\rm W}^n\Gamma(1 + n/k_{\rm W}) with Γ(1.4)=0.887\Gamma(1.4) = 0.887 and Γ(2.2)=1.102\Gamma(2.2) = 1.102, find: ((a)) the mean wind speed ⟨v⟩\langle v\rangle; ((b)) the ratio ⟨v3⟩/⟨v⟩3\langle v^3\rangle/\langle v\rangle^3; ((c)) the flow power density 12ρ⟨v3⟩\tfrac12\rho\langle v^3\rangle for air of density ρ=1.225 kg m−3\rho = 1.225\,\mathrm{kg\,m^{-3}}.

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