Area enclosed within a curve
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I'm trying to find the enclosed area for two curves, shown in the plot titled "Ideal and Schmidt pV Diagrams". I think using the "trapz" function should work but im not sure how to discretise the x-axis, thank you for any suggestions.
V_se=0.00008747;
V_sc=0.00004106;
v=V_sc/V_se;
T_e=333;
T_c=293;
t=T_c/T_e;
phi=pi/2;
T_r=312.6;
%let V_de=1000, V_r=500, V_dc=50
V_de=0.000010;
V_r=0.000050;
V_dc=0.000010;
V_d=V_de+V_r+V_dc;
T_d=324.7;
s=(V_d/V_se)*(T_c/T_d);
B=t+1+v+2*s;
A=sqrt(t^2-2*t+1+2*(t-1)*v*cos(phi)+v^2);
c=A/B;
p_m=101325;
p_max=p_m*(sqrt(1+c)/sqrt(1-c));
p_min=p_m*(sqrt(1-c)/sqrt(1+c));
delta=atan((v*sin(phi))/(t-1+v*cos(phi)));
alpha=0:0.2:2*pi;
for k = 1:numel(alpha)
p(k) = (p_m*sqrt(1-c^2))/(1-c*cos(alpha(k)-delta));
end
figure
plot (alpha,p)
xlabel('\alpha')
ylabel('p')
% min = min(p);
alpha=0:0.2:2*pi;
for k = 1:numel(alpha)
V_total(k) = (V_se/2)*(1-cos(alpha(k)))+(V_se/2)*(1+cos(alpha(k)))+(V_sc/2)*(1-cos(alpha(k)-phi))+V_d;
end
figure
plot (alpha,V_total)
xlabel('\alpha')
ylabel('V_total')
alpha=0:0.0001:2*pi;
for k = 1:numel(alpha)
p_1(k) = (p_m*sqrt(1-c^2))/(1-c*cos(alpha(k)+delta));
V_1_total(k) = (V_se/2)*(1-cos(alpha(k)))+(V_se/2)*(1+cos(alpha(k)))+(V_sc/2)*(1-cos(alpha(k)-phi))+V_d;
end
p_start = (p_m*sqrt(1-c^2))/(1-c*cos(0-delta));
P_mid = (p_m*sqrt(1-c^2))/(1-c*cos(pi-delta));
figure
plot (V_1_total,p_1)
xlabel('V_total')
ylabel('p')
hold on
plot(Vv1, p_2(Tv1,Vv1), 'LineWidth',2)
plot(Vv1, p_2(Tv2,Vv1), 'LineWidth',2)
plot(Vv1(1)*[1 1], p_2([Tv1(1) Tv1(end)],[1 1]*Vv1(1)), '-k', 'LineWidth',2)
plot(Vv1(end)*[1 1], p_2([Tv2(1) Tv2(end)],[1 1]*Vv1(end)), '-k', 'LineWidth',2)
title('Ideal and Schmidt pV Diagrams')
hold off
% I = trapz(V_1_total,p)
5 Comments
dpb
on 6 Dec 2019
Update the code in the original; then use the 'Code' button to format it legibily/neatly...
Probably if you just generated the final data to create the plot and attached it would be simpler--how you generated the curves is really of not much import here I think...unless you want to try symbolic integration (and I don't have toolbox to try).
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