How this is calculated
Hydro power is weight falling: density times gravity times flow times head, in kilograms per cubic meter, meters per second squared, cubic meters per second and meters. Water is 1,000 and gravity 9.81.
Reclamation writes it in field units: theoretical horsepower is flow in cubic feet per second times head in feet, divided by 8.8, at 746 watts to the horsepower.
Gross head is the drop from the intake water surface to the turbine. Net head is what survives the penstock, and only net head makes power.
Pipe loss is Hazen-Williams as EPANET writes it: 4.727, times C to the power of minus 1.852, times diameter in feet to the power of minus 4.871, times length, times flow in cubic feet per second to the power of 1.852. C is 140 to 150 for new plastic and steel, 130 to 140 for cast iron.
Worked example 100 ft gross head, 60 GPM, 400 ft of 3-inch PVC. Friction takes 3.6 ft, leaving 96.4 ft net: 1,090 W hydraulic, and at 70 percent turbine and 85 percent generator 649 W continuous, 15.6 kWh a day. In 2-inch pipe the loss becomes 26 ft.
Worked example 30 m gross head, 4 L/s, 120 m of 75 mm PVC. Friction takes 1.3 m, leaving 28.7 m net: 1,126 W hydraulic, and at 70 percent turbine and 85 percent generator 670 W continuous, 16.1 kWh a day. In 50 mm pipe the loss is 9.4 m, nearly a third of the drop.
Quick answers
How much power will a small stream actually make?
Net head times flow. At 60 percent water-to-wire, feet times gallons per minute times 0.113 is watts: 100 ft and 60 GPM is about 680 W.
How do I measure head and flow without survey gear?
A hose full of water with a gauge on the low end reads head at 2.31 ft per psi. Flow comes from a bucket and a stopwatch, or a weir.
Why does penstock diameter matter so much?
Loss scales with diameter to the power of about 4.87, so halving the pipe multiplies the head lost inside it by roughly 29.
Does a micro-hydro system still need a battery?
Yes, for surge rather than energy. A turbine cannot lift its output for the two seconds a pump takes to start, so the battery covers peaks.
Measuring head with a hose, flow with a bucket
Run a hose from the intake pool to the turbine site, fill it, cap the low end with a gauge and read the static pressure: psi times 2.31 is feet, bar times 10.2 is meters.
Under about 40 GPM, dam the stream so all of it falls through a pipe and time a bucket. Above that, use a weir: Reclamation's Cone equation for a fully contracted 90 degree V-notch is 2.49 times the head on the notch in feet raised to 2.48, for 0.05 to 4.25 cubic feet per second, with a lower limit of 0.2 ft on the notch.
Measure in the dry month. A stream at 200 GPM in April and 25 in September is a 25 GPM scheme with a good spring.
The pipe is the project
The exponent on diameter is 4.871. Dropping from 3-inch to 2-inch at the same flow multiplies the loss by 7.2; halving the diameter multiplies it by 29.
Aim to lose about 10 percent of gross head in the pipe and treat 20 percent as the point where the penstock is eating the project. Those two thresholds are what the verdict line above reacts to.
Buried plastic at C 150 costs less than the bigger turbine it would take to make the loss back.
Matching the machine to the site
Impulse machines fire a jet at buckets in open air and want pressure. The Department of Energy calls the Pelton a machine for very high heads and low flows, the cross-flow one for larger flows and lower heads. A Turgo sits between them, passing more water than a Pelton wheel of the same size.
Reaction machines run full of water and work the pressure difference across the blades: propeller and Kaplan for a few feet of drop and plenty of water, and the Francis, which the same source places at 130 to 2,000 ft.
The site chooses. A 6 ft drop with 500 GPM and a 300 ft drop with 12 GPM make similar power and share no parts.
Head against flow: continuous watts
Net head down the side, flow across the top, at 60 percent water-to-wire. Any cell times 24 is kWh a day.
| Net head | 10 GPM | 25 GPM | 50 GPM | 100 GPM | 250 GPM | 500 GPM |
|---|---|---|---|---|---|---|
| 5 ft | 6 | 14 | 28 | 57 | 141 | 283 |
| 10 ft | 11 | 28 | 57 | 113 | 283 | 566 |
| 20 ft | 23 | 57 | 113 | 226 | 566 | 1,130 |
| 50 ft | 57 | 141 | 283 | 566 | 1,410 | 2,830 |
| 100 ft | 113 | 283 | 566 | 1,130 | 2,830 | 5,660 |
| 200 ft | 226 | 566 | 1,130 | 2,260 | 5,660 | 11,300 |
| 400 ft | 453 | 1,130 | 2,260 | 4,530 | 11,300 | 22,600 |
Watts, continuous. The average US home bought 10,791 kWh in 2022 (Energy Information Administration), about 30 a day: 1,250 W continuous, which 100 ft of net head reaches at roughly 110 GPM.
| Net head | 0.5 L/s | 1 L/s | 2 L/s | 5 L/s | 10 L/s | 25 L/s |
|---|---|---|---|---|---|---|
| 2 m | 6 | 12 | 24 | 59 | 118 | 294 |
| 5 m | 15 | 29 | 59 | 147 | 294 | 735 |
| 10 m | 29 | 59 | 118 | 294 | 588 | 1,470 |
| 20 m | 59 | 118 | 235 | 588 | 1,180 | 2,940 |
| 30 m | 88 | 177 | 353 | 883 | 1,770 | 4,410 |
| 60 m | 177 | 353 | 706 | 1,770 | 3,530 | 8,830 |
| 120 m | 353 | 706 | 1,410 | 3,530 | 7,060 | 17,700 |
Watts, continuous. A 10 kWh day is 420 W continuous, which 20 m of net head reaches at about 3.6 L/s; the 20 m, 5 L/s cell leaves headroom.
Intake, trash rack and winter
Water enters through a trash rack, then a screen, then a settling box where sand drops out. Size the rack so water creeps through it: a large screen lets the current carry leaves past, a small one packs solid in the first storm.
Winter is the test. A buried, full, moving penstock rarely freezes, but the intake pool skins over and slush ice can blind a screen overnight.
The fixes are dull: bury below the frost line, draw from under the ice, slope the rack so it sheds, and build access for raking in the dark.
Why the battery stays
Hydro arrives as a constant trickle and loads do not. A 650 W scheme makes 15.6 kWh a day and still cannot start a well pump.
So the battery covers peaks and the inverter is sized by the largest motor in the house, the arithmetic behind the well pump calculator and starting watts. It also needs a dump load, usually a water heater, so the turbine stays loaded when the battery fills.
Against sun, hydro trades peak for persistence: matching the worked example with panels takes roughly 5 kW of array at 4.2 peak-sun-hours, or 7 kW at the 3.0 assumed for northern Europe, and neither runs at midnight.
Water rights come before arithmetic: in the US the right to divert is state law, so ask your state water agency and the Federal Energy Regulatory Commission before anything else.
Water rights come before arithmetic: abstraction is licensed nationally under the Water Framework Directive, so ask your regulator, for example the Environment Agency, before anything else.
Sources
Bureau of Reclamation, Hydroelectric Power pamphlet (theoretical horsepower, 746 W per horsepower) and Water Measurement Manual, chapter 2 (psi to feet of water) and chapter 7 (Cone equation). US Environmental Protection Agency, EPANET 2.2 User Manual, tables 3.1 and 3.2 (Hazen-Williams). Department of Energy, Types of Hydropower Turbines (Francis, 130 to 2,000 ft). Energy Information Administration, residential electricity sales, 2022. Checked September 2026.
Go deeper
Weigh the site against solar, wind, hydro and a generator, then take the daily kWh into the off-grid solar sizing calculator. If the stream is also the household supply, choosing a water source and the battery bank calculator finish it.