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Hydro & marine calculator

Micro hydro calculator: power, yearly energy and the right turbine

Turn head and flow into kilowatts, kWh per month and payback. The model includes real penstock friction, part-load turbine efficiency, seasonal flow and a residual (environmental) flow, and recommends a turbine type.

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Results

10.1 kW electrical at the design flow of 60 L/s and 27.5 m net head, about 64,558 kWh a year (capacity factor 73%). Best-suited turbine: Cross-flow (Banki–Michell). Pays back in about 5 years.
Electrical power at design flow
10.1kW
Cross-flow (Banki–Michell) · overall η 57% water-to-wire
Annual energy
64,558kWh
177 kWh per day on average
Capacity factor
73.3%
6,420 full-load hours
Net head
27.5m
friction + minor loss 2.54 m (8.5%)
Design flow
60L/s
mean 60 L/s · residual 6 L/s
Hydraulic power (net)
16.2kW
gross 17.7 kW = ρgQH
Penstock velocity
1.91m/s
Re 293,849 · f 0.0149
Year-1 value
€9,684
Payback
4 yr 11 mo
capex 45,248 €
LCOE
0.063€/kWh
IRR 21.3%
CO₂ avoided per year
25.8t
Monthly energy and stream flow
Turbine suitability score for your site

Turbine selection (net head, design flow)

TurbineHead range (m)Flow range (m³/s)Peak ηMin. flowFits your site
Cross-flow (Banki–Michell)2–2000.01–1072–80%15%✓ selected
Turgo10–3000.002–1078–85%15%✓
Pelton10–1,8000.001–5080–88%10%✓
Propeller / fixed-blade1.5–300.05–50078–88%70%✓
Francis10–7000.1–1,00084–92%40%—
Kaplan (double-regulated)1.5–400.3–1,00084–91%20%—
Archimedes screw1–100.1–1575–82%20%—

Monthly breakdown

MonthStream flow (L/s)Turbine flow (L/s)LoadPower (kW)Energy (kWh)
Jan8760100%10.17,107
Feb8460100%10.16,419
Mar7860100%10.17,107
Apr635795%9.636,586
May514575%7.755,477
Jun393355%5.683,882
Jul302440%4.072,874
Aug272135%3.532,496
Sep332745%4.63,149
Oct514575%7.755,477
Nov8160100%10.16,878
Dec9660100%10.17,107
  • Use a long-term mean flow. A single measurement in a wet month will badly overstate output.
  • Monthly flow follows a generic “Temperate rain-fed (winter high)” pattern. Real streams vary day to day, so a flow-duration curve from gauging data gives a better estimate.
  • Residual flow requirements are set by your water authority (often Q347 or 5–20% of mean flow). Permits, intake works and grid connection usually dominate small-hydro costs.

How this micro hydro calculator works

On paper, hydropower is the easiest renewable to calculate: falling water releases energy in direct proportion to its mass and the height it drops. Simple calculators still overestimate badly, because they leave out friction in the penstock, seasonal flow and how turbines behave at part load. This one models all three.

  1. Flow. Enter a measured mean flow, or estimate it from catchment area × rainfall × runoff coefficient. A residual (environmental) flow stays in the stream. What’s left varies month by month following a seasonal pattern: rain-fed, snow-melt, monsoon, Mediterranean or spring-fed.
  2. Net head. Penstock friction comes from the Darcy–Weisbach equation with a Colebrook friction factor for your pipe material and diameter. Minor losses at the intake, bends and valves are added on top.
  3. Turbine. Pelton, Turgo, cross-flow, Francis, Kaplan, propeller and Archimedes-screw turbines are scored against your net head and design flow, and the best fit is picked unless you choose one yourself. Each family has its own peak efficiency, part-load curve and minimum flow. A propeller turbine stops below about 70% of its design flow, while a Pelton keeps running down to 10%.
  4. Energy and money. Monthly power × hours × availability, then payback, LCOE and IRR.

The formula

P = ρ × g × Q × H_net × η_turbine × η_generator × η_drive

H_net = H_gross − f × (L / D) × v² / 2g − ΣK × v² / 2g Q_turbine,month = min(Q_design, Q_stream,month − Q_residual) E_year = Σ_months P_month × hours × availability

Here ρ = 1,000 kg/m³ and g = 9.81 m/s². Typical micro-hydro efficiencies are 72–88% for the turbine, 85–92% for the generator and 95–97% for drive and controls, so water-to-wire efficiency usually lands at 55–75%.

Worked example: a farm stream

The defaults describe a stream with a mean flow of 60 L/s and 30 m of gross head. Water runs through 150 m of 200 mm HDPE pipe; the flow pattern is temperate (high in winter) and 10% is left as residual flow.

  • Pipe velocity is 1.9 m/s and friction plus minor losses take 2.5 m (8.5%) of the head, leaving 27.5 m net.
  • The best-scoring turbine is a cross-flow (a Turgo would also fit), with a micro-scale peak efficiency near 72%.
  • At the 60 L/s design flow the system delivers about 10 kW electrical, or 57% water-to-wire.
  • In winter the turbine runs at full flow. By late summer the stream is down to under 30 L/s and output falls to about a third. Over the year that adds up to roughly 64,600 kWh (capacity factor 73%).
  • At 4,500 €/kW the installation costs about €45,000. If each kWh is worth €0.15, payback takes about five years and the LCOE is near €0.06/kWh.

How to read the results

  • Electrical power at design flow: the nameplate rating you would order.
  • Annual energy and capacity factor: what the site is really worth once seasonal variation, residual flow and downtime are counted.
  • Net head and penstock velocity: if losses go above 10–15% or velocity above about 3 m/s, try a larger pipe in the penstock calculator.
  • Turbine suitability chart and table: the head and flow envelope of each family. A tick means your site falls inside it.
  • Monthly table: when the turbine runs at part load, and when it stops below its minimum flow.

Typical values

Turbine Net head Flow Peak efficiency (micro → large) Part-load behaviour
Pelton 10–1,800 m (best > 50 m) 1 L/s – 50 m³/s 80–92% excellent, down to 10% flow
Turgo 10–300 m 2 L/s – 10 m³/s 78–88% very good
Cross-flow 2–200 m 10 L/s – 10 m³/s 72–85% flat curve, simple and rugged
Francis 10–700 m 0.1–1,000 m³/s 84–94% poor below ~40% flow
Kaplan 1.5–40 m 0.3–1,000 m³/s 84–93% good (double-regulated)
Propeller 1.5–30 m 0.05–500 m³/s 78–90% needs > 70% flow
Archimedes screw 1–10 m 0.1–15 m³/s 75–85% good, fish-friendly

Tips to get more from your site

  • Measure flow through a dry season. A bucket-and-stopwatch, float or salt-dilution measurement in August is worth more than any rainfall estimate.
  • Maximise head, not pipe length. Moving the intake uphill often adds more head than friction, though it’s worth checking in the penstock calculator.
  • Pick the design flow on purpose. Sizing for the mean flow keeps utilisation high. Sizing for 1.3–1.5× the mean captures more winter energy, at the price of more months at part load.
  • Use two units (or a multi-jet Pelton) when flows swing widely, so one machine can still run efficiently in the dry season.
  • Keep the intake clean. Debris on the trash rack can cost several metres of head overnight.

Limitations

The monthly flow patterns are generic. A real flow-duration curve from gauging data, or from a nearby gauged catchment, is far more accurate, and because flow varies day to day even a monthly model slightly overstates output. The catchment method is a rough ±50% estimate. Turbine envelopes and efficiencies are typical published values, not a specific manufacturer’s hill chart. Civil works, permits, fish passage and grid connection often dominate the cost, and they enter only through your cost per kW.

Method & assumptions

Power: P = ρ · g · Q · Hnet · ηturbine · ηgenerator · ηdrive, with ρ = 1,000 kg/m³ and g = 9.81 m/s². Net head = gross head − friction loss (Darcy–Weisbach with Colebrook friction factor for your pipe's roughness) − minor losses (ΣK·v²/2g). Turbine peak efficiencies are typical published values, lower for micro units (<100 kW); part-load efficiency follows a family-specific curve (Pelton and cross-flow are flat, Francis drops quickly, propeller turbines need >70% flow), and each turbine stops below its minimum flow. Monthly flow = mean flow × seasonal factor − residual flow, capped at the design flow. Energy = Σ monthly power × hours × availability.

Frequently asked questions

How do you calculate hydro power?
P = ρ × g × Q × H × η: water density (1,000 kg/m³) × gravity (9.81 m/s²) × flow (m³/s) × net head (m) × overall efficiency. For micro hydro a quick rule is P (kW) ≈ 5 to 7 × Q (m³/s) × H (m), which corresponds to 50–70% water-to-wire efficiency.
How much power can I get from a small stream?
It depends on head as much as flow. 10 L/s falling 50 m gives about 3 kW electrical; the same 10 L/s falling 5 m gives only 0.3 kW. A stream of 100 L/s with 10 m of head yields around 5–6 kW, enough for several homes if it runs all year.
Which hydro turbine should I use?
High head and low flow suit impulse turbines: Pelton above about 50 m, Turgo from roughly 10 to 300 m. Cross-flow turbines handle medium heads (3–100 m) and varying flows well. Low heads (below about 10–15 m) with large flows call for Kaplan or propeller turbines or an Archimedes screw. At larger scales, Francis turbines dominate medium heads.
What is the difference between gross head and net head?
Gross head is the vertical height between the intake water level and the turbine. Net head is what's left after friction in the penstock and losses at the intake, bends and valves. A well-designed micro-hydro penstock loses 5–15% of the gross head.
How much does a micro hydro system cost?
Installed costs range widely, from about 2,000 to over 10,000 per kW (EUR or USD), depending on head, civil works, pipeline length and grid connection. High-head sites come out cheapest per kW, since the turbine and pipe are small for the power they deliver.
Do I need a permit for micro hydro?
Almost always. Typical conditions are water abstraction and impoundment licences, fish-passage requirements and a minimum residual flow that must stay in the stream. Talk to your national environment or water agency before you buy equipment.
How much energy does micro hydro produce per year?
A well-designed run-of-river plant runs day and night, so capacity factors of 40–75% are common, far above solar or wind. A 10 kW system can produce 35,000–65,000 kWh a year, provided the stream keeps flowing through the dry season.

Sources & references

  1. ESHA — Guide on How to Develop a Small Hydropower Plant (European Small Hydropower Association)
  2. IRENA — Renewable Power Generation Costs in 2023 (hydropower chapter)
  3. Paish, O. (2002). Small hydro power: technology and current status. Renewable and Sustainable Energy Reviews 6(6)
  4. US Department of Energy — Planning a Microhydropower System

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