Question

Peristaltic pumps deliver highly viscous fluids to networks of pipes/tubes. Solve the system given the set of linear equations using the matrix solver in MATLAB, GaussNaive and GaussPivot. Assume the following pipe sections all have the same diameter and lengths. Q1 = 5. Q3 + 2Q4 – 2Q2 = 0 Q3 = Q4 +Q5 Q1 = Q2+Q3 3Q7 – 206 = 0 Q5 +226 – 204 = 0) Q5 = Q6 +Q7 li | lz | Os Q2 Qul lol Qı

Answer 1

Given equations are: 75 204+Q3 +294 9.-Q-By -204481226 -0 8-04-QS = 0 -24+24 50 . 95-Q6-Qzzo Writing the given linear equations in - AX= B form. 0 0 0 0 0 To -2 1 2 0 0 0 0 0 - 0 10 0 0 0 - To-o * ๐ 1 20 - T 1 0 0 -2 1 2 0 1 4 4 0 0 0 0 0 -2 0 0.01 + oooo ♡ T O oo T' 0 0 O 'c

For this problem no pivoting is needed, so Gauss naive and gauss pivot method are same.

MatLab program for matrix solver

clear all
clc
close all
% given data
A=[1 0 0 0 0 0 0
   0 -2 1 2 0 0 0
   1 -1 -1 0 0 0 0
   0 0 0 -2 1 2 0
   0 0 1 -1 -1 0 0
   0 0 0 0 0 -2 3
   0 0 0 0 1 -1 1];
b=[5;0;0;0;0;0;0];
Q=A\b

Screenshot

Ona 1 clear all 2 clc 3 close all 4% given data 5 A=[1 0 0 0 0 0 0 0 -2 1 2 0 0 0 1 -1 -1 0 0 0 0 0 0 0 -2 1 2 0 0 0 1 -1 -1 0 0 10 0 0 0 0 0 -2 3 11 0 0 0 0 1 -1 1]; 12 b=[5;0;0; 0; 0; 0;0]; 13 Q=A\b

Save the above program and execute it.

Result

Q = 5.0000 2.8049 2.1951 1.7073 0.4878 1.4634 0.9756

Gauss elimination method

clear all
clc
% inputs
% no. of equations
n=7;
% setting A and b matrix
A=[1 0 0 0 0 0 0
   0 -2 1 2 0 0 0
   1 -1 -1 0 0 0 0
   0 0 0 -2 1 2 0
   0 0 1 -1 -1 0 0
   0 0 0 0 0 -2 3
   0 0 0 0 1 -1 1];
b=[5;0;0;0;0;0;0];
% agumented matrix
AB=[A b];
% forward elimination
for i=1:1:n-1
    for j=i+1:n
AB(j,:)=AB(j,:)-(AB(j,i)./AB(i,i)).*AB(i,:);
    end
end
% backward elimination
X=zeros(n,1);
X(n,1)=AB(n,n+1)/AB(n,n);
for i=n-1:-1:1
    summ = AB(i,n+1);
    for j = i+1:n
        summ = summ-AB(i,j)*X(j,1);
    end
X(i,1)=summ/AB(i,i);
end
fprintf('The results is: Q=\n');
disp(X);

Screenshot

10 1 clear all 2 clc 3% inputs 4% no. of equations 5 n=7; 6% setting A and b matrix 7 A=[1 O O O O O O 0 -2 1 2 0 0 0 1 -1 -1 0 0 0 0 O O O -2 1 2 0 ll 0 0 1 -1 -1 0 0 12 OOOOO -2 3 13 0 0 0 0 1 -1 1]; 14 b=[5;0;0; 0;0;0;0]; 15 % agumented matrix 16 AB=[Abl; 17% forward elimination 18 for i=1:1:n-1 19 for j=i+1:n 20 AB(j, :)=AB(j,:) - (AB(j,i)./AB(i,i)). *AB(i,:); 21 end 22 end 23% backward elimination 24 X=zeros (n,1); 25 X(n,1)=AB (n, n+1)/AB(n,n); 26 for i=n-1:-1:1 27 summ = AB(i,n+1); for j = i+1:n 29 summ = summ-AB(i,j)*X(),1); 30 end 31 X(i,1)=summ/AB(i,i); 32 end 33 fprintf('The results is: Q=\n'); 34 disp(X); 28

Save the above program and execute it.

Result

The results is: Q= 5.0000 2.8049 2.1951 1.7073 0.4878 1.4634 0.9756

I hope this will help you.