Question

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 90-m-diameter (D) blades at that location. Take the air density to be 1.25 kg/m3. The mechanical energy of air per unit mass is .05 Numeric ResponseEdit Unavailable. .05 correct.kJ/kg. The power generation potential of the wind turbine is

Answer 1

Answer:

$X=3976.078202kW \approx 3976kW$

Explanation:

From the question we are told that

Wind speed$V_w=10m/s$

Turbine blade diameter $D=90m$

Air density  $\tau=1.25kg/m^3$

Mechanical energy $K.E =0.05kJ/kg$

Generally the power generation potential of the wind turbine X is mathematically given as

  $X=m'*K.E$

Where

$m'=\tau *\pi*D^2/4*V$

$m'=1.25 *\pi*90^2/4*10$

$m'=79521.56404kg/s \approx 79521.5kg/s$

Therefore

$X=m'*K.E$

$X=79521.56404*0.05$

$X=3976.078202kW \approx 3976kW$

$X=4.0MW$