Jason, here is a sketch of what you need to do. First, you need to create a function
y = f(S,Q,W,etc.)
in a separate file will all your independent variables as arguments (there seem to be quite a few). This function will need to accept a vector for S, which means a lot of your code will need to be rewritten. In particular, the if/then statement could be put in side a loop or replaced by logical indexing (see Matrix indexing in MATLAB):
Vcr = w*2.05;
ix = ((Us*d/v)>1.2) && ((Us*d/v)<70);
Vcr(ix) = w*((2.5/(log10(Us(ix)*d/v)-0.06))+0.66); %EDITED
and you need to replace * by .* and ^ by .^ everywhere (assuming that all the other variables are scalars). The last line of the function would be
y=(w*Cts*10^(I/J))/(V-Vcr)-S;
The solution of the equation y=0 is the S you are after.
Then define an inline function
g = @(S) f(S,Q,W, ...)
(see Anonymous functions). You need to provide values for all the arguments except S before defining this function. Finally, solve using fzero:
S = fzero(g,S0)
where S0 is your guess for the value of S that solves the equation. To help you with finding a good guess, you could plot g(S) against S first.
