This is both a math question and a algorithm question. Not a programming question.
My question is that if we got a problem to solve, for example hydraulic spool gap theory.
Where the function of leakage flow of this gap is:
$$q_l = \pi v r h_0 + \frac{\pi h_0^3 \Delta p}{6 \eta l}[1+ 1.5(\frac{e}{h_0})^2]$$
Where:
- $\eta$ = dynamic viscosity [$Ns/m^2$]
- $v$ = relative velocity [$m/s$]
- $r$ = radius [$m$]
- $h_0$ = mean gab height $\frac{h_1+h_2}{2}$ [$m$]
- $e$ = eccentricity [$m$]
- $p_i$ = pressure [$Pa$], $i = 0, 1$
- $\Delta p = p_1 - p_0$
- $l$ = length [$m$]
- $q_l$ = leakage flow [$m^3/s$]
The question are now:
- Can I use if-statements and while-loops etc. for minimizing this gap function?
- If I have measurements of e.g the flow, pressure etc. Can I use the data to minimize the gap function then?
My theory is to just "looping thought" the function by using algorithms, which will generates data. Then search in the data for the optimal solution? Is that possible?
If YES: Is there any special methods to use? Or can I just use simple knowledge of MATLAB-programming and try to find the minimum?