Werner;
The method that you have presented in my humble opinion is far too complicated. The answer is so simple its almost embarrassing. I had some lunch recharged my brain and then it occurred to me. The answer as I always suspected is to do with the velocity. All I needed to do was relate h the height of the water to the velocity of discharge i.e. V(h) and then the rest is trivial. The answer was starring me and you right in the face but I could not see it and you were far too busy fixing my sloppy math to probably pick up this fundamental error. One of the problems, I believe, is that MathCad presents error messages that tend to lead one to look in all the wrong places. I have attached the final version for your and others inspection. If you think I have overlooked something please let me know.
Kind regards, Mark
PS
Thank you for all you help I have learned so more about MathCad in the process and this was my secondary aim, in doing this exercise so I am satisfied.