00:01
Hello, here we have to solve the following problem.
00:02
We have to consider a wind turbine with a blade span diameter of 100 meters that is installed at a site subjected to the steady -state winds of 8 meters per second.
00:19
The turbine is 32 % efficient and density of air is 1 .25 kilograms per cubic meter.
00:33
We have to calculate the electric power which can be generated by this turbine.
00:39
Let's solve this.
00:40
So the electric power which is generated equals to the mechanical power multiplied by efficiency over 100%.
00:49
And the mechanical power can be calculated as following.
00:54
So that is mass times speed over 2 and over delta t.
01:00
And on the other hand, that can be this ratio of m over delta t can be written as following.
01:10
That is density of air times volume over 2 delta t and v squared.
01:22
And this product of this volume equals to area, which is pi d squared over 4, multiplied by delta x, by 2, delta t and v squared and here delta x is the length of this air which go through the turbine.
01:47
Therefore this mechanical power can be written as raw pi d squared over 8 multiplied by v cube because delta x over delta t is speed.
02:09
So therefore electrical power equals to pi raw d squared over 8 v cube multiplied by efficiency over 100%.
02:25
Let's calculate it and now let's complete this calculation.
03:14
That is 8 ,042 kilowatts.
03:18
Oh sorry, 8 ,000 and 42 watts...