Answer:
[tex]e_{mec}=162J/kg[/tex]
[tex]P_{potential}=18312480W=18312.5kW[/tex]
[tex]P_{actual}=5493.7kW[/tex]
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:
[tex]e_{mec}=\frac{v^2}{2}\\e_{mec}=\frac{(18m/s)^2}{2} \\e_{mec}=162J/kg[/tex]
For Power generation potential
The generation potential of turbine will determined from the available kinetic energy of air:
[tex]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[/tex]
For Actual power
The actual power generation could be defined as follow as:
[tex]P_{actual}=nP_{potential}\\P_{actual}=0.3*18312.5kW\\P_{actual}=5493.7kW[/tex]
