00:01
In this problem, we're going to be looking at the power generation of a wind turbine.
00:05
So what we want to show is that the power generated by a wind turbine is proportional to the radius of the area that this wind turbine covers, the cross -sectional area.
00:21
So r squared.
00:23
And it's also proportional to the cube of the wind velocity.
00:27
So the wind velocity goes up by factor of two, the power would go up by a factor of eight.
00:36
So how do we show this? well, we can start up by thinking about the kinetic energy of moving air, which is going to be our source of energy here.
00:45
So the kinetic energy of anything is pretty much one half mv squared.
00:51
And v is going to be our air velocity.
00:54
M is going to be the mass of some air, where we know that.
00:57
That mass is equal to density times volume.
01:01
So we can rewrite this as row times v times little v for volume squared.
01:07
I'm gonna put these little guys on here to denote air velocity.
01:12
And so we have our energy here.
01:15
But for power, we know power is the change in energy with respect to some small change in time...