Integrate with two dependent variables and solve a system
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Hello all!
I will try to explain my problem:
I have two equations and two unknowns "w" and "T". One of the equations is an integral from a to b relative to a variable "r". The integral equation contains two terms that are function of both "w" and "r" and this term calls a value on a interpolated plot. Those terms are defined as Cd and Cl.
The equations are the following, knowing that:
- mult_Cl = CL(-((atan(20/(pi*r)) - pi/18) - atan(w/(omega*r)))*180/pi)* omega*r/(sqrt(omega.^2*r.^2+w.^2));
- mult_Cd = CD(-((atan(20/(pi*r)) - pi/18) - atan(w/(omega*r)))*180/pi)* omega*r/(sqrt(omega.^2*r.^2+w.^2));
and
- CL and CD are interpolated functions
T = integral ( rho/2*(omega.^2*r^2 + w.^2)* ( 4 - 2.35294*(r/50 - 0.1)) *( mult_Cl + mult_Cd ),5,50);
T = 2*pi*rho*R.^2*(Vinf - w)*w
----
Where rho, omega, Vinf are known values
I need to solve both T equations at the same time to find a value of "w" for both.
I have never tried that before, so I am kinda lost. Thank you very much!!
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Answers (1)
Torsten
on 9 Nov 2015
Use MATLAB's fzero on the function
f=@(w)integral ( rho/2*(omega.^2*r^2 + w.^2)* ( 4 - 2.35294*(r/50 - 0.1)) *( mult_Cl + mult_Cd ),5,50) - 2*pi*rho*R.^2*(Vinf - w)*w
to get w.
Then insert in one of the above equations to get T.
Best wishes
Torsten.
4 Comments
Torsten
on 10 Nov 2015
The first argument to "integral" must be a function handle, not an expression.
Best wishes
Torsten.
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