# ode45 concentration problem

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Carey n'eville 2021년 1월 3일
댓글: Carey n'eville 2021년 1월 4일
Hello friends I wrote this code because,. But when I run the code, plot is wrong
We have a lake which have zero concentration of organic pollutant C0=0mg/L, but there is an inflow to the lake which contain organic pollutant with a concentration Cin=31mg/L , when we measure the concentration of organic pollutant in the lake when t=15day=5475hr
C5475=12mg/L. I guess It should increase to the Cin=31mg/L
Cin= Concentration which is inflow of the system(lake), it is consumed with a rate k=5*(10^-6)
C=concentration of the lake, because of being complete mix system C=Cout.
V=volume of the lake
Q=inflow and ourflow of the lake
Min=total mass flux which also equal to Q*Cin
r=k.Cin*exp(-k*t)^2 which is second order decay reaction term
Actual complete mix system formula:
V*(dC/dt)=((Q*Cin)-(Q*C)-(r*V))
How to write a proper code for my purpose? Could you help me please, I need your help?
clear all;
clc;
close all;
%15day=365hr*15day=5475hr
C0=0;
C5475=12;
tspan = [0 5475];
[t,C]=ode45(@concentration, tspan, C0);
plot(t,C)
xlabel('time (hr)')
ylabel('Concentration (mg/L)')
function dCdt=concentration(t,C)
k=5*(10^-6);
A=100*10000;
h=2.5;
V=(A*h)/1000;
Q=500000;
Min=15.5*1000000;
Cin=Min/Q;
dCdt=((Q*Cin)/V-(Q*C)/V-(k*(Cin*exp(-k*t)^2)));
end
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Cris LaPierre 2021년 1월 4일
Units? Specifically
• V
• Q
• k

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### 채택된 답변

Cris LaPierre 2021년 1월 4일
편집: Cris LaPierre 2021년 1월 4일
First big error I see is that, assuming your A and h are in meters, you have not correctly converted your to L. . You have divided where you should have multiplied. Try this.
C0=0;
tspan = [0 5475];
[t,C]=ode45(@concentration, tspan, C0);
plot(t,C)
xlabel('time (hr)')
ylabel('Concentration (mg/L)') function dCdt=concentration(t,C)
k=5E-6;
A=100*10000;
h=2.5;
V=(A*h)*1000; % Changed to multiply
Q=500000;
Cin=31; % mg/L
dCdt=((Q*Cin)/V-(Q*C)/V-(k*(Cin*exp(-k*t)^2)));
end
##### 댓글 수: 1표시숨기기 없음
Carey n'eville 2021년 1월 4일
I appreciate to you your answer, it works thank you so much!

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R2020b

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