Small Hydropower & Micro Hydropower

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

Sincerely,
Jess

Hydropower Calculation Example SI & US units

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What are the essential one or two most important things that are blocking you from moving forward with your Hydropower site ideas or plans?

Now is your chance to pipe up about what is the biggest thing you think is preventing you from starting or completing your Small or Micro Hydroelectric project?

For example:  I’m blocked by; ‘Regulations…’, ‘Cash or capital issues…’, ‘Understanding the site…’, ‘Not sure how to proceed with…’, etc. You fill in the missing words in your comment on this post,  Try to keep discussion focused on the  issue that most impacts your progress.

Use the comments on this post to gain or give insight and provide feedback between all the readers.

This is also where a few of our more experienced Renewable Hydropower readers can really help by adding your comments to any threads as you have insight..

Sincerely,
Jess

PS.  This is a great time to think hard about what is really blocking your way forward with hydropower.

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Hydraulic or Water Power comes from the combination of water flow rates and pressure differences.

The power available in a stream of water is given as “P” where:

P = Hydraulic Power

= Efficiency × Pressure difference × Volume rate of water flow

= Joules/Second

= Watts¹

Note:  This is hydro power including hydro turbine efficiency (losses in heat from friction & turbulence.)  P is the power which is the amount of work that can be done (Joules)  in a unit of time (1 second) which is also known as Watts.  Watts have the same units regardless of whether it is Watts in fluid flow or in electricity flow.

In terms of physical parameters the basic gravity driven water power equation becomes -

=  Efficiency × Pressure difference × Volume rate of water flow

Where:

• P = power (J/s or watts)
• η = turbine efficiency
• ρ = density of water (kg/m³) or (lb-mass/ft³)
• g = acceleration of gravity (9.81 m/s²) or (32 ft/s²)
• h = head (m) or (ft). For still water, this is the difference in height between the inlet and outlet surfaces. Moving water has an additional component added to account for the kinetic energy of the flow. The total head equals the pressure head plus velocity head.
• = Water volume flow rate (m³/s) or (ft³/s)

We’ll be revisiting this hydro-energy relationship more in the future.  I have a request to work up an example or two for reference as well.  I’m working on it,  it just takes is a bit of time, and we’ll keep on blogging SmallHydro too…

———-

I have included reference to both metric (SI) and English units above.  In a upcoming post I’ll elaborate on key Hydropower calculations for each system.

Ref 1:  Frank M. White, “Fluid Mechanics,”  McGraw Hill, 1979 , pp 180-188

More information on Water Power can be found on Wikipedia – Water Turbine article.
More on physics of  power found on Wikipedia.

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