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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Dyuman Joshi
Dyuman Joshi 2023-10-31
Why not just sum the discrete values of Pressure-force at each point?
Torsten
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
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")
x = struct with fields:
x1: [1323×1 double]
y = load("y.mat")
y = struct with fields:
y1: [1323×1 double]
p = load("p.mat")
p = struct with fields:
p: [1323×1 double]
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)
Warning: Reached the maximum number of function evaluations (10000). The result fails the global error test.
sol = 37.9349
mean_sol = sol/(pi*(5^2-1^2))
mean_sol = 0.5031
  5 个评论
Torsten
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.
Francesco Brescia
Francesco Brescia 2023-11-2
Thank you very much for the help Torsten, I'll have a better look at trapz.

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