I am trying to derive the Betz factor from scratch and I did it but I just assumed the intial part as being right and now I have some questions about the first step. I have succesfully derived the Betz factor being 0,593 but the initial part, that includes Newton's 2nd law states that:
[math]F = ma = m\frac{\mathrm{d} v}{\mathrm{d} t}=\dot{m}\Delta v=\dot{m}(v_1{}-v_2{})=\rho Sv(v_1{}-v_2{})[/math]
I've never seen someone state that [math]m\frac{\mathrm{d} v}{\mathrm{d} t}=\dot{m}\Delta v[/math] and I don't know what it represents neither mathematically nor physically. Later on from that the maths is very simple, you just substitute from one equation to another, get the final equation, differentiate it by speed ratio, set the differentiated equation equal to zero and find the function maximum which is 0,593. I won't write the whole process here but you can find it on: This link under "Application of conservation of mass (continuity equation)".
It would be very helpful and a piece of crucial information if someone could explain the part I wrote up there to me a bit more into details.
Kind regards and thank you all in advance,
T.
[math]F = ma = m\frac{\mathrm{d} v}{\mathrm{d} t}=\dot{m}\Delta v=\dot{m}(v_1{}-v_2{})=\rho Sv(v_1{}-v_2{})[/math]
I've never seen someone state that [math]m\frac{\mathrm{d} v}{\mathrm{d} t}=\dot{m}\Delta v[/math] and I don't know what it represents neither mathematically nor physically. Later on from that the maths is very simple, you just substitute from one equation to another, get the final equation, differentiate it by speed ratio, set the differentiated equation equal to zero and find the function maximum which is 0,593. I won't write the whole process here but you can find it on: This link under "Application of conservation of mass (continuity equation)".
It would be very helpful and a piece of crucial information if someone could explain the part I wrote up there to me a bit more into details.
Kind regards and thank you all in advance,
T.