Question

At a certain location, wind is blowing steadily at 18 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 80-m-diameter blades at that location. Also, determine the actual electric power generation, assuming an overall efficiency of 30 percent. Take the air density to be 1.25 kg/m3.

Answer 1

Answer:

$e_{mec}=162J/kg$

$P_{potential}=18312480W=18312.5kW$

$P_{actual}=5493.7kW$

Explanation:

Given data

Diameter d=80m

Speed v=18 m/s

Efficiency n=30%

Air density p=1.25 kg/m³

For Mechanical energy of air per unit mass

The power potential of wind per unit mass could be defined as follow:

$e_{mec}=\frac{v^2}{2}\\e_{mec}=\frac{(18m/s)^2}{2} \\e_{mec}=162J/kg$

For  Power generation potential

The generation potential of turbine will determined from the available kinetic energy of air:

$P_{potential}=e_{mec}m\\P_{potential}=e_{mec}pV\\P_{potential}=e_{mec}p\frac{dV}{dt}\\ P_{potential}=e_{mec}pA\frac{dx}{dt} \\P_{potential}=e_{mec}pr^2\pi v\\P_{potential}=(162J/kg)(1.25kg/m^3)(\frac{80m}{2} )^2\pi (18m/s)\\P_{potential}=18312480W=18312.5kW$

For Actual power

The actual power generation could be defined as follow as:

$P_{actual}=nP_{potential}\\P_{actual}=0.3*18312.5kW\\P_{actual}=5493.7kW$