Question

Problems 1. The following equation describes the process of warming a hot tub by adding hot water: IN-ISTART) where is the temperature of the water in the hot tub is the temperature of the water flowing into the hot tub, (130°F) is the initial temperature of the water in the hot tub (65°F) is the hot-water flow rate (5 gpm) is the volume of the hot tub (500 gallons), and is the elapsed time since the hot water started flowing TIN TSTART Create an x-y plot that shows how thehot tub water temperature (T) increases over time (t). Your temperatures should be plotted from 65°F up to 110°F. You may have to extend your time vector until it causes the temperature to exceed 110°F. Identify each major temperature data point (increments of 5°F) on your plot. Add a textual annotation to your plot that lists the approximate time at which the tub's water temperature first reaches 110°F. If the hot-water flow rate was increased to 10 gpm, how long would it take for the water temperature in the tub to reach 110℉? Again, you may have to extend your time vector until it causes the temperature to exceed 110°F Have MATLAB draw a second plot, representing this second set of data on the same graph as the first plot. Add a second textual annotation for the second plot. Include a legend that identifies each plot. a. b.

Answer 1

Please find required MATLAB code along with necessary details in comments below:

clear all; clc; close all;

t=[0:1:180]'; T_IN=130; T_start=65; Q=5; V=500;

% calcualte T for time t
for k=1:length(t)
T(k,:)=T_IN - (T_IN -T_start)*exp((-Q/V)*t(k,:));
end

idx=find(T>=110);
fprintf('It takes %d mins to reach temprature of 110 F.\n',t(idx(1)))
str=sprintf('Time taken to reach 110F');
h1=plot(t,T,'r-');
xlabel('Time (t)'); ylabel('Water Temprature (T)');
ylim([65 110]);

% normalize axis for annotation
xPlot=t(idx(1)); yPlot=T(idx(1));
axPos = get(gca,'Position'); %# gca gets the handle to the current axes
xMinMax = xlim;
yMinMax = ylim;
xAnnotation = axPos(1) + ((xPlot - xMinMax(1))/(xMinMax(2)-xMinMax(1))) * axPos(3);
yAnnotation = axPos(2) + ((yPlot - yMinMax(1))/(yMinMax(2)-yMinMax(1))) * axPos(4);

% mention annotation in graph
ta = annotation('textarrow', [xAnnotation xAnnotation-0.01], [yAnnotation yAnnotation-0.01]);
ta.String = str;

%% Part b
disp('With flow rate=10gpm');
Q=10;
% calcualte T for time t
for k=1:length(t)
T2(k,:)=T_IN - (T_IN -T_start)*exp((-Q/V)*t(k,:));
end

idx=find(T2>=110);
fprintf('It takes %d mins to reach temprature of 110 F.\n',t(idx(1)))
hold on
h2=plot(t,T2,'b-');
legend([h1,h2],{'Q=5','Q=10'}) % legend of the plot

% normalize axis for annotation
xPlot=t(idx(1)); yPlot=T2(idx(1));
axPos = get(gca,'Position'); %# gca gets the handle to the current axes
xMinMax = xlim;
yMinMax = ylim;
xAnnotation = axPos(1) + ((xPlot - xMinMax(1))/(xMinMax(2)-xMinMax(1))) * axPos(3);
yAnnotation = axPos(2) + ((yPlot - yMinMax(1))/(yMinMax(2)-yMinMax(1))) * axPos(4);

% mention annotation in graph
ta = annotation('textarrow', [xAnnotation xAnnotation-0.01], [yAnnotation yAnnotation-0.01]);
ta.String = str;

============================= SCREENSHOT OF CODE

$main_Script.mX clear all clc: close all; t calcualte T for time t | for k=1 : length (t) T (k, : )=TIN- (T-IN -T-start) *exp ( (-Q/V) *t ( k, : ) ) ; end 10 idx=find (T>=110) ; fprintf(It takes %d mins to reach temprature of 110 F.\n,t(idx)) str=sprintf (Time taken to reach 110F); h1-plot (t,T, r- xlabel (Time (t) ylabel (Water Temprature (T) ylim ([65 110]): 12 13 15 16 17 normalize axis for annotatio XPlot=t (idx(1) ) ; yPlot*T (idx(1) ) ; axPos = get (gca, Position); gca gets the handle to the current axes xHinMax = x1im; yMinMax ylim; xAnnotation = axPos (1) + ( (XPlot - xMìnMax (1)) / (xMìnMax (2)-xMìnMax (1)) ) * axPos (3) ; y Annotation = axPos (2) + ( (yPlot - yMìnMax (1) ) / (yMìnMax (2)-yMìnMax (1) ) ) * axPos (4) ; 19 20 21 23 24 25 26 27- mention annotation in graph ta = annotation (text arrow , [xAnnotation ta. String 3tr; xAnnotation-0.01], [yAnnotation y Annotation-0.011);$

========================================= SAMPLE OUTPUT