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

`X=3976.078202kW \approx 3976kW`

Step-by-step 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`