Integrate pressure over area, from dataset points
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Hi, i want to compute the integral over the area of the pressure distribution p(x,y). I have vectors x and y ,say each one of size n by 1,containing the coordinates at which the pressure is known, and a vector of pressures, size n by 1, with the pressure at each coordinate. I thought i could use trapz 2 times to compute the integral first in one direction and then the other, but to do this i would need a Matrix of pressure, instead i have a vector of the same size of the coordinates x and y. I also know that the area I have is an anulus surface, as i can see from plotting using stem3(x,y,p). The coordinates are taken w.r.t the center of the anulus, in cartesian coordinates. Hope you can help me figure this out, thanks.
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Torsten
2023-10-31
编辑:Torsten
2023-10-31
If your suggestion was used, the density of the measurement points had to mirror the areas associated with them. But imagine data accumulating in a certain area while in another, there are almost no measurements. In this case, the weights for the datapoints in the integration couldn't be equally chosen.
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Torsten
2023-10-30
编辑:Torsten
2023-10-30
Maybe you want to get mean pressure over the face. In this case, divide "sol" by area = pi*(5^2-1^2) as done below.
x = load("x.mat")
y = load("y.mat")
p = load("p.mat")
plot(x.x1,y.y1,'o')
F = scatteredInterpolant(x.x1,y.y1,p.p);
fun = @(r,theta)F(r.*cos(theta),r.*sin(theta)).*r;
sol = integral2(fun,1,5,0,2*pi)
mean_sol = sol/(pi*(5^2-1^2))
5 个评论
Torsten
2023-11-1
编辑:Torsten
2023-11-1
Study the example
Multiple Numerical Integrations
under
to learn about the necessary format of your function data in order to use "trapz" for a 2d integration.
If you have problems to make your data compatible with the required format for "trapz", use the "scatteredInterpolant" approach - the setup is easy and the results won't differ significantly in my opinion.
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