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Hydropower Energy calculations and GPM-PSI Unit conversions

Apr 23

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,


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

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