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===== Power Output Equation ===== | ===== Power Output Equation ===== | ||
A common field equation to measure the '''theoretical''' maximum power available in a moving body of water is: | |||
:<math>\, P_{max} = \frac{Q_{max}*H_{max}*e_{max}}{k}</math> | |||
<br>Where: | |||
*P<sub>max</sub>=Maximum Power Available (kW) | |||
*Q<sub>max</sub>=Flow (Volume/time) | |||
*H<sub>max</sub>=Head (Vertical drop in ft) | |||
*e<sub>max</sub>=Efficiency of the turbine (use a value of 1 for max power available) | |||
*K=Unit conversion factor (see table below for some common values) | |||
<div> | |||
{| class="FCK__ShowTableBorders" | |||
|- | |||
| align="center" | '''For Q measured in''' | |||
| align="center" | '''K is equal to''' | |||
|- | |||
| ft<sup>3</sup>/min | |||
| 708 (ft<sup>4</sup>)/(min*kW) | |||
|- | |||
| ft<sup>3</sup>/sec (CFS) | |||
| 11.8 (ft<sup>4</sup>)/(sec*kW) | |||
|- | |||
| l/sec | |||
| 102 (l*ft)/(sec*kW) | |||
|- | |||
| gal/min (GPM) | |||
| 5302 (gal*ft)/(min*kW) | |||
|} | |||
</div> | |||
<br> | |||
To find the '''actual''' power you will get from that moving body of water, calculate P<sub>net</sub> with the following changes made. | |||
:<math>\, P_{net} = \frac{Q_{net}*H_{net}*e_{net}}{k}</math> | |||
Where: | |||
*P<sub>net</sub>= The net power extracted from the river, not including loss in delivery from power station to load (kW) | |||
*Q<sub>net</sub>= Flow (Volume/time) - Only take a portion of the max flow (%<sub>take</sub>). For delicate streams this may be a small percentage of the total flow | |||
**Q<sub>net</sub>=Q<sub>max</sub>*%<sub>take</sub> | |||
*H<sub>net</sub>= Head (Vertical drop in feet) - This is the actual head that you have available, which is primarily comprised of the system drop in water surface level minus losses from friction. Calculate friction loss using tables based on the materials you use for diversion (e.g. PVC) | |||
**Determine equivalent length of pipe by adding actual length of pipe and equivalent lengths of fittings based on tables using pipe size | |||
**Find Frictional Pressure Loss Ratio (FPL) coefficient in ft<sub>loss</sub>/ft<sub>pipe</sub> based upon flow rate and pipe size | |||
**Calculate H<sub>loss</sub>=equivalent length of pipe * FPL | |||
**H<sub>net</sub>=H<sub>max</sub>-H<sub>loss</sub> | |||
*e<sub>net</sub>= Efficiency of the turbine - Always between 0 and 1, usually between .5 and .9 depending on the turbine type and flow rate. A value of 0.78 is a good guess for modern turbines in average conditions | |||
*K=Unit conversion factor (see table above for some common values) | |||
Note that these equations are static in time. You must run these equations with a resolution high enough to cover periods of variation (e.g. monthly river data). | |||
=== Costs === | === Costs === |