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

`e_(mec)=162J/kg`

`P_(potential)=18312480W=18312.5kW`

`P_(actual)=5493.7kW`

Step-by-step 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)=(v^2)/(2)\\e_(mec)=((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(dV)/(dt)\\ P_(potential)=e_(mec)pA(dx)/(dt) \\P_(potential)=e_(mec)pr^2\pi v\\P_(potential)=(162J/kg)(1.25kg/m^3)((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`