📄 chap1_ex4_1.m
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% Chapter 1, Example 4.1
% This m.file computes the numerical values for Table 4.1
% and generates the graph in Figure 4.3
clc; close all; clear all;
dt=0.25;
H0=4;
t(1)=0;
H(1)=H0;
HA(1)=H0;
A=10; R=2; F=5;
fact=1-(dt/(A*R));
tau=A*R;
tfinal=5*tau;
ifinal=round(tfinal/dt);
for i=1:ifinal-1
HA(i+1)=fact*HA(i)+(dt/A)*F;
t(i+1)=i*dt;
end % i
ti=linspace(0,tfinal,1000);
Hi=R*F+(H0-R*F)*exp(-ti/tau);
del=ifinal/50;
plot(t(1:del:end),HA(1:del:end),'r.')
axis([0 100 0 11])
hold on
plot(ti,Hi,'k')
xlabel('\itt \rm(min)','FontSize',11)
ylabel('\itH \rm(ft)','FontSize',11)
text(40,7,'\itH_{\rmA}(\itn\rm), \itn\rm = 0,8,16,..','FontSize',11)
plot(37,7,'r.')
text(40,6,'\itH\rm(\itt\rm)','FontSize',11)
plot([35.5 38.5],[6 6],'k')
text(40,3,'\Delta\itt \rm= 0.25 min','FontSize',11)
title('Approximate and Exact Tank Level vs. Time','FontSize',11)
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