A water distribution system consisting of two centrifugal pumps in two parallel

Question

A water distribution system consisting of two centrifugal pumps in two parallel flow channels is
to be designed. The total flow rate V is the sum of the flow rates Vl and V2 in the two paths.
Therefore,
V = Vl + V2
Also, the characteristics of the two pumps are given in terms of the pressure difference P as
P = P1 - A (Vl)2 P = P2 - B (V2)2
where P1 and P2 are the maximum pressures generated (for no flow conditions) and A, B are
constants. The energy balance, considering elevation change H and the friction losses, gives
P = H + C (V)2
Take the base, or design, values of P1, P2, H, A, B, and C as 520, 725, 125, 7.5, 21 and 5.1,
respectively, in SI units.
Develop script-m or function-m files to achieve the following.
1. For these base values, compute the flow rates and the pressure difference P, using the
Newton-Raphson and the modified Gauss-Seidel (successive substitution) methods.
Elimination may be used to reduce the number of equations to 2 for Newton's method and to 1
(root solving) for the other method.

Explanation / Answer

clc
clear all

N = 21 ; % initialisation
Pi = 1 ;
dt = 0.05;
z=dt* (Pi)^2 ;
dX= 1/(N-1);
y = dt/((dX)^2) ;
d = (1+2*y+z)*ones(N,1);
a = -(y)*ones(N-1,1);
b = -(y)*ones(N-1,1);
x= ones(N,1);
n=0;
stopping_criteria=0;

r =ones(N,1) ; %initial conditio
d(1)= 1; % boundary condition
a(1)= 0; % boundary condition
b(N-1) =-1;
d(N)= 1;
r(N)=0 ;
  
  
while stopping_criteria==0 ,

Mean.Square.difference = 0 ;
xn = x;   
[x] = Tri_diagonal(d,a,b,N,r);

for k=1:1:N
  
m = ((x(k)-xn(k))^2)/(N-1) ;
Mean.Square.difference = Mean.Square.difference+m;

end
Rms.difference = sqrt(Mean.Square.difference) ;
  
if ( Rms.difference)/dt<=10^-3
stopping_criteria=1;
else
stopping_criteria=0;
end

for i=1:1:N-1
r(i)=x(i) ;
  
end
n=n+1;
end

display(Rms.difference);
display(n);

base_temp_derivative = (x(2)-x(1))/dX;
display(base_temp_derivative);
display(x);

i=1:1:N;
plot ((i-1)/(N-1),x(i));
hold all

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.