I am trying to use the trapezoidal rule to compute the flow rate of fluid through a pipe.

Question

Connor Mondock 2022-4-14

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https://ww2.mathworks.cn/matlabcentral/answers/1696170-i-am-trying-to-use-the-trapezoidal-rule-to-compute-the-flow-rate-of-fluid-through-a-pipe

评论： Torsten 2022-4-14

clear
% Velocity distribution function of the pipe
v = 3.9*(1-r./r0).^n;
% Area = pi*r^2
% dA = 2*pi*r dr
% Q = V dA dr
% Value of exponent in velocity distribution function
n = 1/5; 
% Value of radius in the pipe (cm)
r0 = 6; 
% Range over which the integral is to be performed
r = [0,6];
% Now using the trapz method
Q1 = 2.0*pi*trapz(r,v)

It spits out an error after the initialization of the velocity distribution function saying it doesn't recognize the variable 'r', but I don't understand because I stated r as a variable below that.

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VBBV 2022-4-14

编辑：VBBV 2022-4-14

Define equation below vector r

VBBV 2022-4-14

在 MATLAB Online 中打开

clear
% Velocity distribution function of the pipe
% Area = pi*r^2
% dA = 2*pi*r dr
% Q = V dA dr
% Value of exponent in velocity distribution function
n = 1/5; 
% Value of radius in the pipe (cm)
r0 = 6; 
% Range over which the integral is to be performed
r = [0,6];
v = 3.9*(1-r./r0).^n;
% Now using the trapz method
Q1 = 2.0*pi*trapz(r,v)

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Answer 1

Alan Stevens 2022-4-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1696170-i-am-trying-to-use-the-trapezoidal-rule-to-compute-the-flow-rate-of-fluid-through-a-pipe#answer_942705

在 MATLAB Online 中打开

I think it needs to be more like this:

% Velocity distribution function of the pipe
% Area = pi*r^2
% dA = 2*pi*r dr
% Q = V dA dr
% Value of exponent in velocity distribution function
n = 1/5; 
% Value of radius in the pipe (cm)
r0 = 6; 
% Range over which the integral is to be performed
dr = r0/1000;
r = 0:dr:r0;
v = 3.9*(1-r./r0).^n;
% Now using the trapz method
Q1 = 2.0*pi*trapz(v)*dr
Q1 = 122.5092
% True value
vfn = @(r) 3.9*(1-r/r0).^n;
Q2 = 2*pi*integral(vfn,0,r0)
Q2 = 122.5221