How do I plot this graph?

I am heavily struggling to plot the following formula:

, where

x is supposed to be plotted on a logarithmic scale and both and Π are an array of 3 values. Moreover, .

I do not get an error, just weird graphs.

The code I made is the following. Could anyone tell me what I'm doing wrong here? Many thanks :-)

Pi_array = [0.5,1.5,4];

Cf_array = [0.0040,0.0028,0.0014];

K = 0.41;

x = linspace(10,1000);

Re_d=1.0.*10.^4;

w2 = @(x) 3.*x.^2-2.*x.^3;

for i=1:3

figure(2)

Pi2=Pi_array(i);

Cf2=Cf_array(i);

eta2= x.*(sqrt(2)./(sqrt(Cf2).*Re_d));

y2=(1./K).*log(eta2)-((2.*Pi2)./K).*(1-w2(x))+sqrt(2./Cf2);

hold on

semilogx(x,y2)

axis ([10 200 0 35])

end

Answer 1

[David Hill]

Cf= [0.0040,0.0028,0.0014];
Pi= [0.5,1.5,4];
K=0.41;
x = linspace(10,1000);
g =(sqrt(2./Cf)/10000)'.*x;
Re_d=1.0.*10.^4;
w = 3*g.^2-2*g.^3;
y=1/0.41*log(g)-(1-w).*((2*Pi/K)')+sqrt(2./Cf)';
semilogx(x,y);

[Stefan Bras]

Thanks for the fast answer David, you saved my day!

[David Hill]

You should check your equations.

Answer 2

[Abraham Boayue]

% Here is another code that you may find useful.

clear variables
close all
Cf = [0.0040,0.0028,0.0014];
Pi = [0.5,1.5,4];
N  = length(Pi);
k  = 0.41;
M  = 1000;
xa = 10;
xb = 10000;
dx = (xb-xa)/(M-1);
x  = xa:dx:xb;
Y  = zeros(N,M);
for i= 1:length(Pi)
    mu= (1/1000)*sqrt(2/Cf(i))*x;
    w = 3*mu.^2-2*mu.^3 ;
    y = 1/0.41*log(mu)-2*Pi(i)/k*(1-w)+sqrt(2/Cf(i));
    Y(i,:)= y;
end
figure
plot(x,Y,'linewidth',2.5)
% semilogx(x,Y,'linewidth',2.5)
ax = title('y(x)');
set(ax,'fontsize',12);
ax= ylabel('y');
set(ax,'Fontsize',12);
ax = xlabel('x');
set(ax,'Fontsize',12);
axis ([10 400 -2500 500])
grid