MATLAB: Loop answers slightly out from correct values

if else

So in my script, I'm using a loop/ if else function. The values this function spits me out are very close to the Pi values in section 5 of my picture, however they arn't quite the same and I can't figure out Why. As the values get smaller and smaller the difference between the values I get and the answers on the table. However, my last formula of Pr/Rs*TI gives me answers that are correct according to the table in section 5. How is this possible when my Pi (called Pr) values are not correct?

Best Answer

Are the differences significant? We are unable to check all the numbers that went into the calculations given in the text. There is at least one difference between the table at the top of the text and the output table (T5 is given as 270.67 in the former and 270.65 in the latter, though this makes little practical difference). The largest relative error in Pr is only 0.03%
You don't need symbolic maths here, you can solve for Z directly in a single statement - see the listing below. I've tidied up some of the coding as well.
hi = [0 , 11 , 20, 32 , 47, 51 , 71 , 84.852 , 90 ];
Ti = [288.15, 216.65 , 216.65, 228.65 , 270.65, 270.65 , 214.65 , 186.946, 186.946];
ai = diff(Ti)./diff(hi);
go = 9.80666;
Rs = .287054;
B =(go/Rs);
Re = 6356.766;
Pi= 101325.0000;
Pr=Pi;
Hh=diff(hi);
Z = Re*hi./(Re - hi);  % solve for Z directly
for i= 1:length(ai)
    if ai(i) == 0  
       Pr(i+1) = Pr(i).*exp(-B*Hh(i)/Ti(i));  
    else
        Pr(i+1) = Pr(i)*(Ti(i)/(Ti(i)+ai(i)*Hh(i))).^(B/ai(i));
    end
end
fprintf('Z\n')
fprintf('%8.5f\n', Z)
fprintf('\n') 
fprintf('Pr\n')
fprintf('%12.5f\n', Pr)
fprintf('\n') 
 
fprintf('P_at_h\n')
P_at_h = Pr./(Rs.*Ti);
fprintf('%10.5f\n',P_at_h)
fprintf('\n')
% Text values
Prt = [101325.0000, 22632.0587, 5474.8862, 868.0180, 110.9062, 66.9388, 3.9564, 0.3734, 0.1457];
RelativeError = (Pr./Prt - 1)*100;
fprintf('Relative error (percent)\n')
fprintf('%5.4f\n',RelativeError)
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