Iterating to find value S

• Hello I'm fairly new to Matlab and I'm having trouble iterating. I'm trying to find the value S however the equation needed to evaluate it depends on S (second line). What is the best way to find S? Any help would be greatly appreciated :)My code:

V=Q/(W*R); Us = (9.81*R*S)^0.5; if ((Us*d/v)>1.2) && ((Us*d/v)<70); Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66); else Vcr=w*2.05; end

I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w); J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w); S=(w*Cts*10^(I/J))/(V-Vcr);

Answer 1

[Andrew Newell]

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.

[Jason]

I'm very greatful for the response but I'm still very confused.

I didn't really explain what I'm trying to do very well. Hopefully this will be clearer:

1. Assume a value for D.

2. Work out V from V=Q/(W*D) (values Q,W are inputted)

3. Solve S=(w*Cts*10^(I/J))/(V-Vcr)

Where:

I = 5.435-0.286*log10(w*d/v)-0.457*log10(Us/w)

J = 1.799-0.409*log10(w*d/v)-0.314*log10(Us/w)

Us = (9.81*R*S)^0.5;

if Us*d/v is between 1.2 and 70

Vcr=w*((2.5/(log10(Us*d/v)-0.06))+0.66)

Otherwise

Vcr=w*2.05

So Us and as a result I and J depend on S

4. Select another D and repeat the steps

5. Compare computed V*S values and find a minimum value

I tried the following code:

y = MyReverseEquation3(Cts,R,d,v,w,Q,W,V,S0,D)

V=Q/(W*D);

Us = (9.81*R*S)^0.5;

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);

y=(w.*Cts.*10.^(I/J))/(V-Vcr)-S;

g = @(S) f(Cts,R,d,v,w,Q,W,V,S);

S = fzero(g,S0);

end

I get the error code: ‘Undefined function or variable "S".’