Problem $4$: Wind Farm Feasibility Analysis

A proposed wind farm will have $10$ turbines, each with a blade radius of $50$ meters. The average

wind speed at the site is $9\frac{m}{s},$ and the air density is $1\mathrm{.}225k\frac{g}{m^3}.$

$4\mathrm{.}1)$ Calculate the power available in the wind for one turbine.

$4\mathrm{.}2)$ Assuming each turbine operates at $40\%$ efficiency and runs at full capacity $30\%$ of the year,

calculate the total annual energy output for the entire wind farm $($in kWh $).$

$4\mathrm{.}3)$ Considering the energy needs of a nearby town are $12$ million kWh annually, will this wind

farm be sufficient to meet the town's energy demand? Explain your answer with calculations.

Bonus Question $($Optional$)$: Wind Resource Assessment

A region is being evaluated for wind energy potential. The wind speed data collected over one

month shows the following average wind speeds $($in $\frac{m}{s})$ each day:

Week $1$:$7,9,10,8,12,6,7$

Week $2$: $8,9,7,6,10,12,9$

Week $3$: $11,12,13,8,10,9,7$

Week $4$: $6,8,7,10,9,11,12$

Calculate the average wind speed over the month, and use the power equation from Problem $1$ to

estimate the total power available for a wind turbine with a radius of $35$ meters and an air density

of $1\mathrm{.}225k\frac{g}{m^3}.$