1. The formula* for determining CD requires net head to be known, - net head being the water pressure at the entry to the nozzle when it is operating. The very large pressure gauge in the picture, calibrated in metres head of water, provided the means for measuring it. Plumbing it to the manifold required the temporary removal of the upper pelton jet.
2. The formula also requires the flow through the nozzle to be known. This was determined by measuring with a stop watch the time it took for a defined volume of water to pass through the orifice. This defined volume was 429.5 litres. It was known to be this because a drop in water level in the header tank of 104 mm could be calculated to be equal to this volume. The height drop of 104 mm was determined by two knitting needles set exactly with their points that distance apart. The stop watch was started when the surface tension 'grab' to the upper needle was broken and was stopped when broken again at the bottom needle. The inflow of water to the header tank was diverted while each measurement was made. The measurement time varied between 131s for the nozzle with the largest orifice and 20m 11s for the smallest.
3. For 13 nozzles with different sized orifices, paired sets of net head and flow measurements were obtained. The Discharge Coefficient for each nozzle was then calculated and the results, with the flow for each nozzle, plotted in MS Excel:
4. As can be seen, the Discharge Coefficient is not the same for all sizes of nozzle. For the smallest size, nozzle I, where the flow is least, the CD is close to unity** indicating that actual flow is the same as would be expected from an ideal nozzle. But as orifice size increases, the CD falls.
5. The new type of nozzle performs better than the old. Old nozzles had a mean CD of 0.85 whereas the new 0.90.
6.The value of Discharge Coefficient for a nozzle depends on the pressure difference between the pressure of water entering the nozzle and the pressure once it has left through the orifice. So although on my site (which has a pressure head of between 51.5 and 53.6 m depending on flow) the CD has been measured as indicated above, the same nozzle on another site with a different pressure head will have a different CD, though it won't be greatly different .
* Q = CD x Anoz x Sqrt (2g x Hnet) whence CD = Q / (Anoz x Sqrt (2g x Hnet))
** The result obtained was 1.01, i.e. better than unity, which is not possible and represents experimental error.