Last week I received a request for a working example of hydropower calculation procedures. Along with that request was another question asking what the 1/11.8 factor meant when working with feet vs. the 9.800 factor using meters and kW . The latter 9.800 factor was what that reader was familiar with. Please bear with me, there is a lot of interesting math ahead!
I will deal with both of these requests and a little bit more about hydropower efficiency computations in today’s SmallHydro.com blog post.
Part of the mystery hydro conversion factor issue stems from the different measurement units used (SI) or metric vs. (US) or British imperial units. These units of length, volume and time all play a role in getting the “right” answer when computing Small & Micro hydro power. Above all, memorize this relationship:
HydroPower = Efficiency x Pressure drop x Flow rate = η x (ρ · g · h) x Q
Another interesting note shown at the bottom of the chart is that when computing the sites turbine inlet hydrostatic pressure = (rho x g x h) the pressure coefficient value for (rho x g) is quite different for each measurement unit type. This coefficient varies with the inverse of the 4′th power of the length for a given unit, hence all the strange conversion factors, like 1/11.82 for (US- kW) and 9.807 for (SI-kW), etc.
Generally it is best to stick with a single unit standard when working these problems to avoid mistakes! Metric really makes the conversion factors simpler, but the US is still using the British imperial system long after others have moved on, so I include it for comparison. Of interest too is that this site is right on the edge of Small or Micro Hydropower qualification. It would make a nice renewable hydro power addition to a ranch, small village or community.
This handy chart shows an example of a 150 meter hydropower site with 0.095 cubic meters per second flow rate. The British (US) unit equivalents of 492.126 ft and 3.355 CFS are shown computed as well as incorporating both turbine and generator efficiency for accuracy.
Here is a PDF file of the same chart for printout: Hydropower-calculations-metric-si-british-us