a$.$ For a given location, the wind speed at $10$ m and $50$ m heights above ground has been measured to be $\backslash (4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and $\backslash (6\mathrm{.}8\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ respectively. Find the wind speed at $90$ m height.

$[10$ marks$]$

b$.$ A wind turbine has a $3$ MW rated power output at standard air density $\backslash (\backslash$left$(15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\},1\backslash$mathrm$\{$alm$\}\backslash$right$)\backslash ).$ Estimate the change of rated power if the turbine operates at a temperature of $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$[5$ marks$]$

c$.$ For the $3$ MW turbine $($from part b$),$ estimate the change of the rated power relative to the sea level conditions, if the turbine is installed at $2000$ m altitude above the sea.

$[5$ marks$]$

d$.$ A borizontal$-$axis wind turbine with rotor $80$ m in diameter is $\backslash (40\backslash \%\backslash )$ efficient in $\backslash (15\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ wind at $600$ m altitude and $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$

Calculate the total amount of power the wind turbine would produce in those winds.

$[10$ marks$]$

Talite $6\mathrm{.}1$ Dently of Dry Air at a Presmare of $1$ Atregpar$\text{'}$

of Althaily