Cutting an in-between nozzle

In Wales, September and October is when water supply is at its lowest.  It's the time when the water available to my Powerspout is diminishing steadily. 

Such is the series of nozzles I use that as water supply decreases, a step change happens in the amount of water delivered to the turbine every time I put in a nozzle with a smaller orifice.  

But the rate at which the autumn decrease in flow occurs is steady and leisurely, and sometimes the change between two nozzles in my series is too great, - the system gets to miss out on some of the flow of water even though it is there for the taking. It is for this reason I have found myself needing to cut a nozzle which is an 'in-between' size, in-between the size of two existing nozzles. 

The challenge facing me was twofold: first to decide what orifice diameter would deliver the in-between size I was aiming for, and second how to cut that size precisely.

To resolve the first, I needed to understand the relationship between orifice size and flow. Clearly, head pressure determines how much water passes through an orifice, but when considering a single installation, head pressure will remain the same for all sizes of orifice and so doesn't enter into the relationship.**

This leaves orifice size and flow being the only two variables, and knowing these for all the nozzles I use, I plotted one against the other to get the graph below. The mathematical formula defining the relationship of flow (y axis) to orifice diameter (x axis) is conveniently given by the Excel graphing program:

The two red arrows mark the positions of the two nozzles between which there was too big a step, - I needed to cut a nozzle which was as near as possible midway between them, and that would be a nozzle having an orifice of 5.7 mm, giving a flow of 0.73 litres / sec. 

So far so good !

But cutting the nozzle to the required size was not easy.  I do this job on a wood lathe (see here) and if you take off too much the orifice is too big. For this reason my first effort failed and the second almost ended the same way.  In the end, I had to be content with a diameter of 5.8 mm which, according to the graph, will deliver 0.75 l/s. It's the point on the graph marked with a blue arrow.

You might think that such precision in trying to cut a nozzle to an accuracy of 1/10 of a millimetre is over the top, - and you're probably right ! But this 'in between' nozzle will probably be the right one to use for the next 2-3 weeks until the steadily diminishing flow eventually makes it too big to use.  My reckoning is that the extra kWh's of generation it will make possible in that 2-3 weeks, as compared with the smaller nozzle I would have had to use, will make the exercise worthwhile.

Time will tell.

Noted added later: to my surprise, the rains came early; instead of flow diminishing, it started picking up; so the in-between nozzle only found itself in use for 10 days.

**  Head pressure can drop with higher flows if the penstock has too small a bore but having a generously sized penstock and with the meagre flows my turbine takes, head pressure can be taken as constant.
Note that the plot will only be true for sites having the same head as mine, i.e. 53 m, and will not be correct for a site with a different head.