Curve fit not spanning the whole data set

I have the following datasets:

L=1;
D=2*0.02;

V1=[0.00010, 0.00025, 0.00050, 0.00075, 0.00100, 0.00250, 0.00500, 0.00750];
V2=[0.01, 0.10, 0.50, 1.00, 3.00, 5.00, 7.00, 10.00];
V=[V1, V2];

Re=(1000*V*D)/(0.001);

lambda_E=(p*D)./(0.5*1000*L*V.^2);
lambda_HP=64./Re;
lambda_W=1.02*(log10(Re)).^(-2.5);

I want to draw a curve over these points, so I fitted them, using the Curve Fitting Toolbox, to a custom equation, that being: a*(log10(x)).^(-2.5), where 'a' is a coefficient. If there's any other way to create a smooth line that goes over these points please let me know about it. I then exported the corresponding code to a function I'd made earlier. Said code looks as follows:

[xData, yData] = prepareCurveData( Re, lambda_W );

% Set up fittype and options.
ft = fittype( 'a*(log10(x)).^(-2.5)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonLinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = 1.02;

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
plot( Re, lambda_W, 'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' );
h = plot( fitresult );
set(h,LineWidth=1.3,Color='r');

However, when I run the original program in which I use the function, the curve I just mentioned (colored red in the picture) stops past a certain value of the 'Re' axis:

This is the full code of the program and the function, respectively:

L = 1;
D = 2*0.02;

V1 = [ 0.00010, 0.00025, 0.00050, 0.00075, 0.00100, 0.00250, 0.00500, 0.00750 ];
V2 = [ 0.01, 0.10, 0.50, 1.00, 3.00, 5.00, 7.00, 10.00 ];
V = [ V1, V2 ];
logV = log( V );

p1 = [ 0.00247, 0.00619, 0.01250, 0.01890, 0.02550, 0.06770, 0.14800, 0.24000 ];
p2 = [ 0.3400, 8.6500, 116.2070, 370.3552, 2442.9590, 5996.8000, 10924.6200, 21040.5100 ];
p = [ p1, p2 ];
logp = log( p );

fit_logV_logp( logV, logp );

%-------------------------------------------------------------------------------------------

Re = (1000*V*D)/(0.001);

lambda_E = (p*D)./(0.5*1000*L*V.^2);
lambda_HP = 64./Re;
lambda_W = 1.02*(log10(Re)).^(-2.5);

fit_lambda_Re( Re, lambda_E, lambda_HP, lambda_W );

function [fitresult, gof] = fit_lambda_Re(Re, lambda_E, lambda_HP, lambda_W)

%-------------------------------------------------------------------------------------------

% Plot data.
subplot( 1, 2, 2 );
plot( Re, lambda_E, 'o', MarkerSize=4, MarkerFaceColor='g' );
xscale('log');
yscale('log');
hold on;

%-------------------------------------------------------------------------------------------

[xData, yData] = prepareCurveData( Re, lambda_HP );

% Set up fittype and options.
ft = fittype( 'rat01' );
opts = fitoptions( 'Method', 'NonLinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [64, -1];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
plot( Re, lambda_HP, 'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' );
h = plot( fitresult );
set(h,LineWidth=1.3,Color='b');

%-------------------------------------------------------------------------------------------

[xData, yData] = prepareCurveData( Re, lambda_W );

% Set up fittype and options.
ft = fittype( 'a*(log10(x)).^(-2.5)', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonLinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = 1.02;

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
plot( Re, lambda_W, 'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' );
h = plot( fitresult );
set( h, LineWidth=1.3, Color='r' );
hold off;

%-------------------------------------------------------------------------------------------

% Label axes
title('\lambda vs. Re');
xlabel( 'Re' );
ylabel( '\lambda' );
legend( 'Valores experimentales', 'Valores teóricos', 'Hagen-Poiseuille', '', 'White',  'Location', 'NorthEast', 'Interpreter', 'none' );
grid on;

I've double checked every single line of code of my program but nothing seems to be amiss. I also wasn't able to find anyone else with the same problem. Any help would be appreciated.

[Torsten]

Make it easy for us to help: include the complete code that reproduces the problem. I cannot make sense of your description.

Why do you want to fit your data to the White equation ? It's already in the form of the function to be fitted - so "a" should come out to be 1.02.

Further, your fit model is linear in the coefficient a. So a nonlinear fitting tool is not necessary.

L=1;
D=2*0.02;
V1=[0.00010, 0.00025, 0.00050, 0.00075, 0.00100, 0.00250, 0.00500, 0.00750];
V2=[0.01, 0.10, 0.50, 1.00, 3.00, 5.00, 7.00, 10.00];
V=[V1, V2];
Re=(1000*V*D)/(0.001);
lambda_W=1.02*(log10(Re)).^(-2.5);
loglog(Re,lambda_W,'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' );

[the cyclist]

The code you posted doesn't seem to produce the figure you posted (starting with the fact that it does not run, since the variable p is not defined). That makes things much more difficult to debug.

One possibility is that the blue line is exactly overlapping the red one, so you don't see it.

Another possibility is that the values of the red become NaN (due to some numerical problem), and are not plotted.

[Salvador]

Sorry I didn't post the whole code, I'm new to this forum and I thought it would be too much information. And the reason as to why I want to fit my data to White's equation is simply because I want to draw a smooth curve that goes along the points. If there's any other way to do this please let me know.

[Torsten]

And the reason as to why I want to fit my data to White's equation is simply because I want to draw a smooth curve that goes along the points. If there's any other way to do this please let me know.

L=1;
D=2*0.02;
V1=[0.00010, 0.00025, 0.00050, 0.00075, 0.00100, 0.00250, 0.00500, 0.00750];
V2=[0.01, 0.10, 0.50, 1.00, 3.00, 5.00, 7.00, 10.00];
V=[V1, V2];
Re=(1000*V*D)/(0.001);
lambda_W=1.02*(log10(Re)).^(-2.5);
loglog(Re,lambda_W,'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' )
hold on
V = linspace(min(V),max(V),100000);
Re=(1000*V*D)/(0.001);
lambda_W=1.02*(log10(Re)).^(-2.5);
loglog(Re,lambda_W,'r')
hold off

●

[Salvador]

@Torsten

Wow, ok, I'm stupid haha. But for some reason, when I execute this code the same thing happens:

plot( Re, lambda_W, 'o', MarkerSize=3, MarkerFaceColor='k', MarkerEdgeColor='k' );
x = linspace( 1, 1e6, 100000 );
plot( x, 1.02*(log10(x)).^(-2.5), LineWidth=1.3, Color='r' );

[Torsten]

1.02*(log10(1)).^(-2.5) = Inf, and the next value for x in your list is 1+(1e6-1)/99999 which is approximately 11:

x = linspace( 1, 1e6, 100000 )

x = 1×100000

1.0000 11.0001 21.0002 31.0003 41.0004 51.0005 61.0005 71.0006 81.0007 91.0008 101.0009 111.0010 121.0011 131.0012 141.0013 151.0014 161.0014 171.0015 181.0016 191.0017 201.0018 211.0019 221.0020 231.0021 241.0022 251.0023 261.0023 271.0024 281.0025 291.0026

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

That's the first visible value for Re on the red curve.

[Salvador]

@Torsten Yup, fixed it. Thank you.