Working:
Couple of things, u_1 > u_2 so your answer is negative. Also the air volume depends on u_1 as in the youtube.
(edited 1 month ago)
sorry what do you mean by "depends on u_1" - isnt the volume just u_1 x t x pi x r^2
Original post by mosaurlodon
sorry what do you mean by "depends on u_1" - isnt the volume just u_1 x t x pi x r^2
Agreed, but you have a seperate volume for the after. The volume of air before and after should be the same?
well, the volume of air after should just be u_2 x t x pi x r^2? - are you saying that the volumes should be equal because if so, why would that be, or if not, am I missing something?
Original post by mosaurlodon
well, the volume of air after should just be u_2 x t x pi x r^2? - are you saying that the volumes should be equal because if so, why would that be, or if not, am I missing something?
Its the mass of air passing through the blades. Where would the missing mass go to if its different?
the other mass would just collide with the blades right? - to transfer momentum and spin a generator - so are you saying the change in kinetic energy is just the change in mass x change in V.
The change in KE is the difference of KE as in your original working, not the square of the difference in velocities.
The mass before and after will be the same so rho pi r^2 u_1 t so something like the diagram in
https://home.uni-leipzig.de/energy/energy-fundamentals/15.htm
(edited 1 month ago)
I think I roughly understand what the website is saying - A_2 needs to be bigger than A_1 so it can have the same mass when the same time has passed as v_1>v_2.
They worked out the difference in pressure by calculating average velocity over that time to find the length of the cylinder of air that is passing through - but this doesn't seem to work either.
Power* not pressure
The picture was just for inspiration, not to directly apply the formula. You dont know A2 in isaac, I was simply trying to make the point that its not necessarily the same as A1. So as in #8, just use the volume/mass going into the turbine blades for both KEs, as is implied in the hints. After the blades, the speed has dropped but the area is larger.
(edited 1 month ago)
Do it systematically.
You know that the “initial KE” of the wind can be expressed in terms of u1, ρ, A1, and Δt.
Do this for “final KE” in terms of u2, ρ, A2, and Δt.
The “change of KE” is “initial KE” minus “final KE”.
Note that A1 u1 = A2 u2 and the “change of KE” can be expressed in a single area.
I believe you can work from there.
Oh right cool, Ive managed to get the correct answer - thanks both of you.

But how do you know A1 = pi*r^2, in the website its shown in the diagram to be slightly less than "A" - is this just an assumption that you have to make.
Original post by mosaurlodon
Oh right cool, Ive managed to get the correct answer - thanks both of you.

But how do you know A1 = pi*r^2, in the website its shown in the diagram to be slightly less than "A" - is this just an assumption that you have to make.

Which website are you referring to? Not sure what you are asking.
The one that mqb2766 sent https://home.uni-leipzig.de/energy/energy-fundamentals/15.htm - in this image it shows A1 as slightly smaller than area of the windmill "A"
Original post by mosaurlodon
The one that mqb2766 sent https://home.uni-leipzig.de/energy/energy-fundamentals/15.htm - in this image it shows A1 as slightly smaller than area of the windmill "A"
tbh, I didnt even notice that. As above, I simply posted it for you to think that the area after is larger than the area before, so the mass/volume is the same. The isaac hint was reasonably clear about what they wanted as an answer.
(edited 1 month ago)
Original post by mosaurlodon
Oh right cool, Ive managed to get the correct answer - thanks both of you.

But how do you know A1 = pi*r^2, in the website its shown in the diagram to be slightly less than "A" - is this just an assumption that you have to make.

Original post by mosaurlodon
The one that mqb2766 sent https://home.uni-leipzig.de/energy/energy-fundamentals/15.htm - in this image it shows A1 as slightly smaller than area of the windmill "A"

When I am writing reply#13, I am using what you are showing in reply#9.

The problem that Isaac Physics has set up is “slightly” different from the one that this website has described.
I don’t think we can just use “copy and paste method” or “plug and play method” to make the connection.