An anemometer mounted $10$ m above a surface with crops, hedges, and shrubs, shows a wind

speed of $5$ m$/$s$.$ Assuming $15$C and $1$ atm pressure, determine the following for a wind turbine

with hub height $80$ m and rotor diameter of $80$ m:

$($a$)$ Estimate the wind speed and the specific power in the wind $($W$/$m$2)$ at the highest point that

the rotor blade reaches. Assume no air density change over these heights.

$($b$)$ Repeat $($a$)$ at the lowest point at which the blade falls.

$($c$)$ Compare the ratio of wind power at the two elevations using results of $($a$)$ and $($b$)$ and

compare that with the ratio obtained using Equation:

$($d$)$ What would the power density be at the highest tip of the blade if we include the impact of

elevation on air density? Assume the temperature is still $15$C$.$ Does air density change seem

worth considering in the above analysis?