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Matlab:
This is a program that will determine (a) the flow rate distribution in a loop network system by the Hardy-Cross method and (b) the total head at ach node. Parameters are given, and they are follows; allow for a maximum of ten loops with a maximum of ten lines in a loop, calculate the flow rates before the total head with respect to the give dimensions of the created program.
A test case 1 is given with known flow rates distribution and total head values; this given case will be tested with the created Matlab program, once this is tested and it function properly, it will be apply to the following pipe system where the values will be randomly generated.
MATLAB code for the first system of pipes
%Project1test.m
%EML 4127 (Applied Thermal Fluids)
%Manuel Armatrading & Mattew Lawrence
clear;
clc;
%Input/Known Data
NL = 3 %Number of Loops
NJ = [4 4 4] %Number of Lines in Each Loop
ID = [2 3 0 0;0 0 0 1;0 0 0 1] %Identifies Which Line is a Common Line
Qin = 10.8; %Flow Rate at inlet
EPSLN = 0.0001; %Maximum allowable difference in flow rates
g = 32.2; %Gravitational acceleration
p=1.94;
u=1.082*10^(-5);
e=.00085
D1 = 10/12; %Pipe # 1 Diameters (in Feet)
D2 = 12/12; %Pipe # 2 Diameters (in Feet)
D3 = 14/12; %Pipe # 3 Diameters (in Feet)
D4 = 16/12; %Pipe # 4 Diameters (in Feet)
%Assumes no minor losses
%Define matrices which describe pipe diameters and pipe lengths
ZL = [10560 15840 10560 15840; 15840 13200 10560 10560;...
15840 15840 15840 15840];
D = [D4 D2 D3 D4;D4 D3 D2 D4;D2 D1 D2 D2];
K= [0 0 0 0 ; 0 0 0 0 ; 0 0 0 0];
%Initial Guess for Flow Rates
Q = [3 1.5 -1.6 -4; 3.8 1.7 0.3 -3; 1.8 0.4 -1 -1.5] %Flow Rate (gpm)
%% ======================================================================%
%Start value for flow difference (1 was chosen randomly)
err=1;
%Index for the while loop
IW=0;
while err> EPSLN %Sets condition that as long as difference is
%greater than EPSNL the loop will run.
IW=IW+1;
for i=1:NL
for j=1:NJ
Re(i,j)=p*abs(Q(i,j))/(pi/4*(D(i,j))^2)*ZL(i,j)/u;
f(i,j)=1.325/(log(e/3.7/D(i,j)+5.74/(Re(i,j))^.9))^2;
dfdQ(i,j)=(13.69*(e/3.7/D(i,j)+5.74/(Re(i,j))^.9)^(-1))/...
((Re(i,j))^2*abs(Q(i,j))*log(e/...
3.7/D(i,j)+5.74/(Re(i,j))^.9));
A(i,j)=8*ZL(i,j)/(pi^2*g*(D(i,j))^5);
B(i,j)=(8*K(i,j))/(pi^2*g*(D(i,j))^4);
%Calculation of head loss
if Q(i,j)>0;
HF(i,j)=A(i,j)*(Q(i,j))^2*f(i,j)+B(i,j)*Q(i,j)^2;
DHDQ(i,j)=2*A(i,j)*Q(i,j)+...
A(i,j)*(Q(i,j))^2*dfdQ(i,j)+...
2*B(i,j)*Q(i,j)+B(i,j)*(Q(i,j))^2*dfdQ(i,j);
elseif Q(i,j)==0
HF(i,j)=0;
DHDQ(i,j)=0;
else
HF(i,j)=-(A(i,j)*(Q(i,j))^2*f(i,j)+B(i,j)*Q(i,j)^2);
DHDQ(i,j)=-(2*A(i,j)*Q(i,j)+...
A(i,j)*(Q(i,j))^2*dfdQ(i,j)+...
2*B(i,j)*Q(i,j)+B(i,j)*(Q(i,j))^2*dfdQ(i,j));
end
SHF(i)=sum(HF(i,:));
SDHDQ(i)=sum(DHDQ(i,:));
DELQ(i)=-SHF(i)/SDHDQ(i);
HFo(i,j)=HF(i,j);
end
end
for i=1:NL
for j=1:NJ
if ID(i,j)==0
NEWQ(i,j)=Q(i,j)+DELQ(i);
elseif ID(i,j)==911
NEWQ(i,j)=Q(i,j);
else
NEWQ(i,j)=Q(i,j)+DELQ(i)-DELQ(ID(i,j));
end
err=abs(NEWQ(i,j)-Q(i,j));
Q(i,j)=NEWQ(i,j); end
end
if IW>100
break
end
IW;
end
%% Total Head Calculation for each node %%
for i=1:NL
disp('enter head at node 1 of loop')
HPo(i)=input('')
HP(i,1)=HPo(i);
for j=1:NJ(i)
if j~=1
HP(i,j)=HP(i,j-1)-HFo(i,j-1);
end
end
HP
end
fid=fopen('Test_results.dat','w')
fprintf(fid,'TEST CASE RESULTS\n');
fprintf(fid,'\n\n');
fprintf(fid,'\n\n Flow Rate Distribution\n');
fprintf(fid,' LOOP # | LINE 1 LINE 2 LINE 3 LINE 4 \n');
fprintf(fid,'*****************************************************************
**********\n');
for i=1:NL
fprintf(fid, '\n%5.0f | ', i);
for j=1:NJ
fprintf(fid,'\t %7.3f ', Q(i,j) );
end
fprintf(fid, '\n');
end
fprintf(fid,'\n\n Head Loss at each node \n');
fprintf(fid,' LOOP # | NODE 1 NODE 2 NODE 3 NODE 4 \n');
fprintf(fid,'*****************************************************************
**********\n');
for i=1:NL
fprintf(fid, '\n%5.0f | ', i);
for j=1:NJ
fprintf(fid,'\t %7.3f ', HP(i,j) );
end
fprintf(fid, '\n');
end
fprintf(fid,'\n\n Numbers of Iterations :');
fprintf(fid,'%7.3f ', IW );
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MATLAB code for the second system of pipes
%Project1.m
%EML 4127 (Applied Thermal Fluids)
%Manuel Armatrading and Mattew Lawrence clear clc
NL = 3; %Number of Loops
NJ = [5 4 4]; %Number of Lines in Each Loop
ID = [0 0 0 1 1; 1 1 0 0 0; 1 0 0 1 0];
%Identifies Which Line is a Common Line
Qin = 5; %Flow Rate at inlet
EPSLN = 0.0001; %Maximum allowable difference in flow rates
g = 32.2; %Gravitational acceleration
p=1.46;
u=1.082*10^(-5);
e=.00085;
D1 = 10/12; %Pipe # 1 Diameters (in Feet)
D2 = 10/12; %Pipe # 2 Diameters (in Feet)
D3 = 10/12; %Pipe # 3 Diameters (in Feet)
D4 = 10/12; %Pipe # 4 Diameters (in Feet)
D5 = 10/12;
D6 = 10/12;
D7 = 10/12;
D8 = 10/12;
D9 = 10/12;
D10= 10/12;
D11= 10/12;
D12= 10/12;
%Assumes no minor losses
%Define matrices' which describe pipe diameters and pipe lengths
ZL = [2000 2000 2000 1000 1000; 1000 1600 1000 1600 0; 1000 1600 1000 1600 0];
D = [D1 D3 D9 D7 D4; D4 D6 D5 D2 0; D7 D10 D8 D6 0];
K= [.40 .75 .40 .40 .40; .40 .40 .40 .75 0; .40 .40 .75 .40 0];
%Initial Guess for Flow Rates
Q = [2.1, 2.1, 2.9, 1.5, 0.3; 0.3, 1.2, 2.6, 2.4, 0; 1.5, 1.4, 1.4, 1.2, 0];
%Start value for flow difference (1 was chosen randomly)
err=1;
%Index for the while loop
IW=0;
while err> EPSLN %Sets condition that as long as difference is
%greater than EPSNL the loop will run.
IW=IW+1;
for i=1:NL
for j=1:NJ
Re(i,j)=p*abs(Q(i,j))/(pi/4*(D(i,j))^2)*ZL(i,j)/u;
f(i,j)=1.325/(log(e/3.7/D(i,j)+5.74/(Re(i,j))^.9))^2;
dfdQ(i,j)=(13.69*(e/3.7/D(i,j)+5.74/(Re(i,j))^.9)^(-1))/
...
((Re(i,j))^2*abs(Q(i,j))*log(e/
...
3.7/D(i,j)+5.74/(Re(i,j))^.9));
A(i,j)=8*ZL(i,j)/(pi^2*g*(D(i,j))^5);
B(i,j)=(8*K(i,j))/(pi^2*g*(D(i,j))^4);
%Calculation of head loss
if Q(i,j)>0;
HF(i,j)=A(i,j)*(Q(i,j))^2*f(i,j)+B(i,j)*Q(i,j)^2;
DHDQ(i,j)=2*A(i,j)*Q(i,j)+
...
A(i,j)*(Q(i,j))^2*dfdQ(i,j)+
...
2*B(i,j)*Q(i,j);
elseif Q(i,j)==0
HF(i,j)=0;
DHDQ(i,j)=0;
else
HF(i,j)=-(A(i,j)*(Q(i,j))^2*f(i,j)+B(i,j)*Q(i,j)^2);
DHDQ(i,j)=-(2*A(i,j)*Q(i,j)+
...
A(i,j)*(Q(i,j))^2*dfdQ(i,j)+
...
2*B(i,j)*Q(i,j));
end
SHF(i)=sum(HF(i,:));
SDHDQ(i)=sum(DHDQ(i,:));
DELQ(i)=-SHF(i)/SDHDQ(i);
HFo(i,j)=HF(i,j);
end
end
for i=1:NL
for j=1:NJ
if ID(i,j)==0
NEWQ(i,j)=Q(i,j)+DELQ(i);
elseif ID(i,j)==24
NEWQ(i,j)=Q(i,j);
else
NEWQ(i,j)=Q(i,j)+DELQ(i)-DELQ(ID(i,j));
end
err=abs(NEWQ(i,j)-Q(i,j));
Q(i,j)=NEWQ(i,j); end
end
if IW>100
break
end
IW;
end
%% Total Head Calculation for each node %%
for i=1:NL
disp(
'enter head at node 1 of loop'
)
HPo(i)=input(
''
)
HP(i,1)=HPo(i);
for j=1:NJ(i)
if j~=1
HP(i,j)=HP(i,j-1)-HFo(i,j-1);
end
end
HP
end
fid=fopen(
'Test_results1.dat'
,
'w'
)
fprintf(fid,
'TEST CASE RESULTS\n'
);
fprintf(fid,
'\n\n'
);
fprintf(fid,
'\n\n Flow Rate Distribution\n'
);
fprintf(fid,
' LOOP # LINE 1 LINE 2 LINE 3 LINE 4 \n'
);
fprintf(fid,
'*****************************************************************
**********\n'
);
for i=1:NL
fprintf(fid, '\n%5.0f | '
, i);
for j=1:NJ
fprintf(fid,
'\t %7.3f '
, Q(i,j) );
end
fprintf(fid, '\n'
);
end
fprintf(fid,
'\n\n Head Loss at each node \n'
);
fprintf(fid,
' LOOP # | NODE 1 NODE 2 NODE 3 NODE 4 \n'
);
fprintf(fid,
'*****************************************************************
**********\n'
);
for i=1:NL
fprintf(fid, '\n%5.0f | '
, i);
for j=1:NJ
fprintf(fid,
'\t %7.3f '
, HP(i,j) );
end
fprintf(fid, '\n'
);
end
fprintf(fid,
'\n\n Numbers of Iterations :'
);
fprintf(fid,
'%7.3f '
, IW );
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