Asked by fert
on 14 May 2017

I have been trying to solve an equation of the matrices with the iteration.

- A*PNode=del_node ; [Eq. 1]
- del_node=(L(i)/D(i)) ; [Eq. 2]

The sizes of the matrices are respectively; A [5x6], PNode [6x1], del_node [5x1], L [1X6] and D [1x6].

The first and the last elements of the PNode should be 2 and 6 respectively. How can I find the possible converged values for the D and PNode matrices assuming that A and L are given?

Answer by John D'Errico
on 14 May 2017

Accepted Answer

You cannot do so. Too many unknowns.

PNode has 6 unknowns, but two are given, so only 4 true unknowns.

But you cannot solve for anything without the 6 unknown values of D. So up to 10 unknowns.

Oh, and del_node is completely unknown too. 5 more of them, so 15 unknowns in total.

The second set of equations, relating del_node to D, is of little help, since we can use that to essentially eliminate del_node.

One other point, the second set of equations is meaningless, since you tell us there are 5 elements of del_node. But the elements of del_node are simple ratios or L(i) and D(i). And since there are 6 values in L and D, that means you are trying to stuff 6 points of "stuff" into a 5 pound bag.

Regardless, you cannot solve the problem. No mathematics will give you an answer.

You need to spend some time re-thinking this problem.

Stephen Cobeldick
on 15 May 2017

@fert: change the format.

John D'Errico
on 15 May 2017

Notice the 1e+05* on top. Use the proper display format to be able to see all of the numbers.

format short g

is a good start. You really did get the same result as I did.

fert
on 15 May 2017

Now the hard part, I am basically trying to get the values of the u(and hence D) and PNodes with the While Loop. I am using a contemporary matrix kkk which must be equal to the del_pipe with the residual of the diff. Though I am getting the error of dimensions disagreement.Can you also give a hand on this matter? Also assuming you are an Italian, grazie millie Dottore:)

A = transpose([1 0 0 0 0;0 1 0 0 0; 0 -1 1 0 0; -1 0 0 1 0; 0 0 -1 -1 -1; 0 0 0 0 1]);

f=0.002;g=9.81; rho=1000;del_t=9;cp=4.18;

L =[12 11 8 6 4];Q_node=[210 157 281 150 50];u=ones(1,5);D=ones(1,5);

PNode=zeros(6,1);PNode([1 5])=[2;6];

del_pipe=ones(5,1);kkk=ones(5,1);

diff=del_pipe-kkk;

jj=0;

%%converging the del_pipe and the kkk matrices in order to find the optimum D and PNode

while diff<1e-5

jj=jj+1;

for i=1:1:5

for j=1:1:6

D(i)=sqrt((Q_node(i)*4)/(3*u(i)*cp*rho*9));

del_node(i)=-1*(rho*f*L(i)/D(i))*u(i)^2/2;

del_pipe=transpose(del_node);

kkk(i)=(A(i,j)*PNode(j))+kkk(i);

diff=abs(del_pipe-kkk);

end

end

end

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