Hydropower Calculation Example in Metric (SI) & British (US) units

May 14
2009
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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

Hydropower Calculation Example SI & US units

Written by Jess in: Small & Micro Hydro, Small Hydro News | Tags: , , , , ,

What is Water Power?

May 07
2009
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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 -

P=\eta\cdot\rho\cdot g\cdot h\cdot\dot v =  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.
  • \dot v= 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.

Written by Jess in: Small & Micro Hydro | Tags: ,

Hydropower Energy calculations and GPM-PSI Unit conversions

Apr 23
2009
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Q: Say you want to convert Psi & GPM to kW water power?

A: Good question – unfortunately there are a myriad of Unit conversions, like furlongs per fortnight. ;-)

Follow my round about conversions, I like to focus on the most common formula to start my thinking.
(unfortunately in English Units)

So I stick with the following formula and convert units to fit it. Metric converts too…
I usually think in CFS & Ft head:

I usually start with this formula –>  kW ideal = (CFS flow x Ft head)/11.8

But you have GPM & Psi for units

1 ft head = 0.433 Psi –> (1 ft/.433 psi) x Z Psi = ft head

There are 60 seconds to a minute –> 1 min = 60 sec

There are 7.48 Gal per Cubic Feet volume –> (1 CF /7.48 Gal) x (Gal /sec) = CFS

So say we have 78 Psi -> 78 psi /.433 psi/ft = 180.14 ft head

And now we’re given 1000 GPM = 1000 GPM x 1 Min/ 60 sec = 16.67 GPS

Now convert to CFS -> 16.67 gal/sec /7.48 Gal/CF = 2.23 CFS

Therefore our kW ideal is = (2.23 CFS x 180.14 ft)/11.8 = 34.02 kW Ideal –> Efficiency % not included

To factor efficiency in Multiply x ~72% for water to wire typical. (must use chosen Gen % x Turbine %).

So we get something like 34.02 kW x 72% = 24.49 kW Typical power as a more realistic measure of output potential.

I sure hope this helps,

Jess

DoradoVista, Inc.
PS:  Mileage will vary, there are a lot of issues not modeled here. It is a start though.

Written by Jess in: Small & Micro Hydro, Small Hydro Calculators | Tags: , , , ,

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