MATLAB: Multiply Matrix by scalar variables

equationmatrix manipulation

I am trying to output a plot of C vs v_f, where v_f is a matrix containing all of the x values for my data points. C is dependent on v_f through a system of equations.
I've run into trouble with the matrix multiplication and keep. I just want all the other variables to act as scalars on every x value in v_f, and output every corresponding y value, but I'm getting a matrix multiplication error.
Error using  / 
Matrix dimensions must agree.
Error in FILTRATION2 (line 24)
n_G = ((rho_p - rho_w)*g*(d_p).^2)/(18 * mu * v_f);
This is my script:
    %Ask for input for particle diameter
    d_f = input('Enter particle diameter in um');
    d_p =(d_f)*10^-6; %convert to m
    %Define Vector for Filtration Velocity
    v_ff = [1:.1:25] ; %m/h
    v_f = (v_ff)/3600; %m/s
    %Define Known Variables
    L = 1; %m

    E = 0.42; 
    a = 1;
    Ha = 10^-20; %J
    d_c=(0.0005); %m
    rho_p = 1020; %kg/m^2

    rho_w = 998.2; %kg/m^2
    g = 9.81; %m/s^2
    mu = .001002; %Ns/m^2
    k_B = 1.381*10^-23; %J/K
    T = 293; %K
    %Define Dependent Variables
    n_I = (3/2)*(d_p / d_c).^2;
    n_G = ((rho_p - rho_w)*g*(d_p).^2)/(18 * mu * v_f);
    n_D = 0.9*((k_B*T)/(mu * d_p * d_c * v_f)).^(2/3);
    X = n_I + n_G + n_D;
    %Define C/Co
    C = exp(((-3/2)*(1-E)*X*a*L)/d_c);
    %Plot C/Co
    plot(v_f,C);
    xlabel('Filtration Velocity (m/h)');
    ylabel('C/Co');
    title('Filter Performance with __ um')
Any help is appreciated on how I can go about solving this problem. Normally I would use excel but this Thank you!

Best Answer

You need to vectorise the division (replace ‘/’ with ‘./’). Then it works:
... CODE ..
%Define Dependent Variables
n_I = (3/2)*(d_p / d_c).^2;
n_G = ((rho_p - rho_w)*g*(d_p).^2)./(18 * mu * v_f);
n_D = 0.9*((k_B*T)./(mu * d_p * d_c * v_f)).^(2/3);
X = n_I + n_G + n_D;
%Define C/Co
C = exp(((-3/2)*(1-E)*X*a*L)/d_c);
%Plot C/Co
plot(v_f,C);
xlabel('Filtration Velocity (m/h)');
ylabel('C/Co');
title(sprintf('Filter Performance with %.1f \\mum', d_f))
I didn’t copy all your code to my Answer, only the part that needed help. I also got the impression you wanted ‘d_f’ to be displayed in the title, so I added that.
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