In the last diary entry I suggested I know what flow each of my nozzles delivers; that the figure for each can be calculated from a formula; that the accuracy of the result given by that formula depends rather too much on the value assigned to two inputs: the nozzle discharge coefficient (Cd) and the net Head (Hn).
Today, I've been doing an experiment to check the accuracy of the figure for Cd I've been assuming these past three years, - and I've found it's way out; the true flow from each nozzle is significantly less than I've been supposing; for me, and perhaps for some other Powerspout operators, this has important implications as I'll go on to show, but first the experiment:
It involved measuring flow rate by stopping the inflow to the header tank and measuring the time it took for the level to drop a measured amount; with knowledge of the dimensions of the tank, the depth dropped and the time it took, calculating the flow rate was easy. Small errors enter because the flow will change as the water level drops (but change only to a tiny extent), and because the internal dimensions of the tank are complicated by internal flanges (a 'best-guess' correction was incorporated).
To get a precise measurement of the drop in water level, two 3 mm knitting needles were mounted in a bit of wood, rigidly fixed to the tank; the tips of the needles were at different levels, a difference which could be measured to 0.02 mm with a vernier caliper; timing started when the falling water level broke the 'grab' on the tip of the higher needle, - the 'grab' being the attachment to the tip of the needle caused by surface tension, - and ended when it was broken on the lower placed needle:
Three runs were made and all provided near identical results: for the nozzle I was using it took 5 mins and 46.7 secs for the water level to drop from one needle tip to the other; calculation gave the flow rate as 1.25 litres per second whereas before I had thought it was 1.29 l/s.
Now you might think this difference to be small but its effects are big; using the figure for flow rate measured today and using it in the formula to do a 'back calculation' of Cd, instead of Cd being 0.91 as I had previously been assuming, it comes out at under 0.88.
Re-calculating the flow for each of my nozzles using a Cd of 0.88 makes each have a flow less than I had been reckoning on; what does this mean in the real world? - it means two things:
- when I thought I was delivering the maximum flow my abstraction licence allows (3 l/s), in fact I was delivering less than this; for the future, delivering a true 3 l/s will mean more power when operating at the top limit of flow.
- 'whole system efficiency' improves with this new information and this makes to be less the factor used in the annual calculation of the total volume of water abstracted, the so-called Hydro Abstraction Factor (HAF), - used to calculate, from the kWh's produced, the volume of water abstracted; my HAF drops from 13 m³ / kWh to 12 m³ and the effect of this is to reduce the likelihood of my going over the volume I'm allowed to abstract in a 12 month period.
As carried out today, the test to verify Cd was performed using just one nozzle. The question remains as to whether the value of Cd changes with nozzles having different orifice sizes; so I'll repeat the experiment as opportunity arises to use nozzles with bigger, or smaller, orifices.
Just at the moment though, it's so dry here that an opportunity to use bigger might be a while in coming.