Height vs Time Plot with Variable

Hi,

I have a Height vs Time plot for a tank which has 1 inlet and 2 outlets. I want to plot Height v Time with multiple lines with varying alpha values. I have created the code to plot the line for 1 alpha value but am unsure how to add multiple lines to show different values. The alpha values will be 0.01:0.01:0.2.

Any help will be much appreciated.

function dhdt = G_20_tankf1(t,h)
% G_20_tankf1: Tank level model
%Derivative function solution for Method 1

% Tank model parameters and chonstants
A = 8.0;             %M^2
CV1 = 2;             %(m^3/min)/(kPa^0.5)
P0 = 100;            %kPa
P1 = P1function(t);  %kPa
P3 = 100;            %kPa
rho = 1000;          %kg/m^3
g = 9.81;            %m/s^2
alpha = 0.01;

% Algebraic equations for F1, F2, P2 and CV2 have been substituted 
% into the differential equation for dh/dt to create a pure ODE system:

dhdt = 1/A*(CV1*sqrt(P1-P0-rho*g*h/1000) - 3*h*sqrt(P0+rho*g*h/1000-P3) - alpha*g*h);




% G_20_tanksim1: Method 1

%Extra Parameters
tf = 72;           %h
h0 = 2 ;           %m

% Solve the DAE
opts = odeset('RelTol',1e-5);
[t,h] = ode45(@G_20_tankf1,[0 tf],h0,opts);

% plot the graph
plot(t,h)
title('G20tanksim1')
xlabel('Time (h)')
ylabel('Level (m)')
grid on

Answer 1

[madhan ravi]

% G_20_tanksim1: Method 1
%Extra Parameters
tf = 72;           %h
h0 = 2 ;           %m
% Solve the DAE

opts = odeset('RelTol',1e-5);
for alpha= 0.01:0.01:0.2
[t,h] = ode45(@(t,h)G_20_tankf1(t,h,alpha),[0 tf],h0,opts);  %function call
figure
plot(h,t)  % height vs time
% plot the graph
title('G20tanksim1')
xlabel('Time (h)')
ylabel('Level (m)')
grid on
end


function dhdt = G_20_tankf1(t,h,alpha)       %function definition
% G_20_tankf1: Tank level model
%Derivative function solution for Method 1
% Tank model parameters and chonstants
A = 8.0;             %M^2
CV1 = 2;             %(m^3/min)/(kPa^0.5)
P0 = 100;            %kPa
P1 = P1function(t);  %kPa
P3 = 100;            %kPa
rho = 1000;          %kg/m^3
g = 9.81;            %m/s^2
% Algebraic equations for F1, F2, P2 and CV2 have been substituted 
% into the differential equation for dh/dt to create a pure ODE system:
dhdt = 1/A*(CV1*sqrt(P1-P0-rho*g*h/1000) - 3*h*sqrt(P0+rho*g*h/1000-P3) - alpha*g*h);
end

[Wes Staveley]

Hi Madhan,

Thankyou for your reply!

Your answer has worked thanks, but it displays each different alpha value on a seperate graph. Is there a way to plot them all on the same graph with a key for example?

Thanks again for your quick response.

[madhan ravi]

just remove the line figure and put hold on after plot command , if my answer helped make sure to accept the answer and give a vote :)

[Wes Staveley]

Have done now. Thanks again!

[madhan ravi]

Anytime :)

[Wes Staveley]

Hi Madhan,

I have 1 more question:

Do you know how to add an automated legend to show each alpha value with a title for the legend of 'Alpha'?

My current solution is to write the following but I imagine there is a simpler way.

Thanks again

legend ('0.01','0.03','0.05','0.07','0.09','0.11','0.13','0.15','0.17','0.19');

[madhan ravi]

Yes it does exist but at the moment I am having trouble finding it , sorry .