I'm not sure how to formulate this in MC. I want to have a function calculate area. However, this area calculation has a minimize procedure built in to find the angle that minimizes the area. So, a flow area is a function of valve stroke and this angle that results from the stroke. Easy enough when I define stroke length:
But when I want everything as a function of stroke I can't get anything to work. I'm after something like this, but making things of a function of Stroke and Beta causes problems.
3.1 files attached
Here's the paper if anyone anyone is interested or wants to visualize what I'm trying to do.
Calculating Throttling Area | Pneumatics content from Machine Design
Here is a way to calculate the factors you see in the table in that article which seems to work in Mathcad 15
Prime seems to be limited and insists to always solve for ALL arguments of the function. So a nasty workaround is necessary.
When we build the table in that article we see, that the values, especially for small angles alpha, differ significantly. Not sure why.
Thank you Werner. Using your example I did get a function to work. (Although I struggle to figure out why the work-around works)
It is very sensitive to the starting guess. Starting with 1 deg caused it to be wrong sometimes and very slow. But 5 deg seems to work well through the stroke.
Yes, I also noted the sensitivity concerning the guess.
I tried an adaptive guess for beta (50% of alpha in the screenshot) but still was not able to duplicate the table of correction factors in that article.