Question No$.7$:

Grade:

$125$

$[$CLO

Select a wind turbine hub height and a rotor diameter such that the generated electrical power is enough to supply a pumping system that needs $100$ MW$.$

Given conditions:

Wind speed $($u$)$: $9\frac{m}{s}$ at $10$ m height

Air density: $1\mathrm{.}225k\frac{g}{m}3$

Surface roughness: $0\mathrm{.}2$ m

Clearance height $(h_c)$: $30m$

Wind shear coefficient $()$: $\frac{1}{4}$

Rated speed: $12\frac{m}{s}$

Efficiency of the Gears system: $90\%$

Efficiency of the electrical generator: $90\%$

Models to be used:

$u=u_1(\frac{x}{z_1}{)}^{}$

$C_p=\frac{u^3}{u_{\text{r}\text{u}\text{t}\text{e}\text{d}}^3}$

$P_{WT}=u^3(\frac{1}{2}{R}^2)C_p{}_{\text{g}\text{e}\text{a}\text{r}}{}_{\text{e}\text{l}\text{e}\text{c}}$