How do i find the intersection between two curves?

clear all
close all
d=10*10^-3; %----rördiameter i meter 
L=20; %-----längd rör
ks=0.3; %----material
Q=0:0.1:2.5; %----volymflöde L/min
Qf=Q/(60*1000); %----gör om till m^3/s
ny=0.661*10^-6; %----kinematisk viskositet
ra=992.2;   %-----densitet
r=(d/2)*10^3; %----rörradien i mm 
engf=0; %------engångsförluster - påverkar dynamisk uppf.höjd

v=Qf*4/(pi*(d^2));
Red=v*d/ny;

if Red<2300
    lam=64./Red;
else
    lam=1./(1.8*log(6.9./Red+(ks/(7.42*r)).^1.11)).^2;
end 


H=(1/(2*9.807)).*(v.^2).*(lam*L/d+engf); %Uppf.höjd Systemkurva

figure(1)
plot(Q,H, 'k','LineWidth',2); %Systemkurva
hold on 
xlabel('Q Volymflöde [L/min]');
ylabel('H Uppfodringshöjd');

%Värden för pump 80 mm diameter

HE=[0.7
    0.69
    0.679
    0.668
    0.656
    0.643
    0.629
    0.614
    0.598
    0.582
    0.565
    0.546
    0.527
    0.507
    0.486
    0.463
    0.44
    0.416
    0.39
    0.364
    0.337
    0.308
    0.278
    0.247
    0.216
    0.183];

plot(Q, HE, 'b', 'LineWidth',2); %Pumpkurva

Hi!

How do I find the exact coordinates for the intersection between those curves?

I've tried with intersect, but I can't get it to work!

Answer 1

[Stephan]

Hi,

usually this can be aproximated with quadratic functions - so you can use polyfit and polyval to calculate functionsthe describing your system and the pump. After this the values are calculated by using this functions and added to the plot (drawn as squares in the corresponding color) - i think it is a good enough result. Now you know your system and your pump functions, which can be used in fzero to calculate the intersection point, that is shown by the red circle in the plot:

close all
d=10*10^-3; %----rördiameter i meter 
L=20; %-----längd rör
ks=0.3; %----material
Q=0:0.1:2.5; %----volymflöde L/min
Qf=Q/(60*1000); %----gör om till m^3/s
ny=0.661*10^-6; %----kinematisk viskositet
ra=992.2;   %-----densitet
r=(d/2)*10^3; %----rörradien i mm 
engf=0; %------engångsförluster - påverkar dynamisk uppf.höjd
v=Qf*4/(pi*(d^2));
Red=v*d/ny;
if Red<2300
    lam=64./Red;
else
    lam=1./(1.8*log(6.9./Red+(ks/(7.42*r)).^1.11)).^2;
end 
H=(1/(2*9.807)).*(v.^2).*(lam*L/d+engf); %Uppf.höjd Systemkurva
figure(1)
plot(Q,H, 'k','LineWidth',2); %Systemkurva
hold on 
xlabel('Q Volymflöde [L/min]');
ylabel('H Uppfodringshöjd');
%Värden för pump 80 mm diameter
HE=[0.7
    0.69
    0.679
    0.668
    0.656
    0.643
    0.629
    0.614
    0.598
    0.582
    0.565
    0.546
    0.527
    0.507
    0.486
    0.463
    0.44
    0.416
    0.39
    0.364
    0.337
    0.308
    0.278
    0.247
    0.216
    0.183]';
plot(Q, HE, 'b', 'LineWidth',2); %Pumpkurva

% Aproximation of the pump with a 2.order polynomial
vals_pump = polyfit(Q,HE,2);
fun_pump = polyval(vals_pump,Q);
plot(Q,fun_pump,'sb')

% Aproximation of the pump with a 2.order polynomial
res_system = polyfit(Q,H,2);
fun_system = polyval(res_system,Q);
plot(Q,fun_system,'sk')

% solve with fzero
intersection_point = fzero(@(Q) polyval(vals_pump,Q) - polyval(res_system,Q),2);
scatter(intersection_point, polyval(vals_pump,intersection_point),'or','filled')
hold off
fprintf('The intersection point is: Q = %1.5f with H = %.5f units.\n'...
    ,intersection_point, polyval(vals_pump,intersection_point))

With the resulting plot:

Best regards

Stephan