Hydro power in watts is 9.81 times flow in liters per second times head in meters times the overall efficiency, and the shortcut of flow times head times 7 is that formula with an efficiency of about 0.71. At 5 L/s and 10 m the shortcut gives 350 watts, while a homemade system at an efficiency of 0.3 gives only 147 watts.
Part of Micro-Hydro Turbine
Hydro power is the weight of water falling per second multiplied by the height it falls, reduced by every loss between the intake and the wires.
The Power Of Falling Water Is Weight Per Second Times Height
One liter of water has a mass of one kilogram. If Q liters fall every second, Q kilograms per second lose potential energy of g × H joules each, where g is 9.81 m/s² and H is the head in meters. A joule per second is a watt, so the hydraulic power is:
P = 9.81 × Q × H × η
| Symbol | Meaning | Unit |
|---|---|---|
| P | electrical output | watts |
| Q | flow through the turbine | liters per second |
| H | net head, the height the runner actually uses | meters |
| η | overall efficiency, the product of all losses | 0 to 1 |
| 9.81 | gravity | m/s² |
In pure SI units, with Q in cubic meters per second, the same law reads P = ρ × g × Q × H × η, with ρ = 1,000 kg/m³ for water. For 5 L/s, which is 0.005 m³/s, at 10 m and η = 0.7: 1,000 × 9.81 × 0.005 × 10 × 0.7 = 343 watts.
The Factor 7 Is 9.81 Multiplied By About 0.71
The carrier writes P = Q × H × 7. Setting 9.81 × η = 7 gives η = 7 ÷ 9.81 = 0.71, the carrier’s “typical overall efficiency of a well-built micro-hydro system”. The factor 7 folds every loss into one number, so it should be paired with a head measured without separately subtracting losses. Illustrative parts that multiply to roughly that figure are 0.95 for the pipe and intake, 0.85 for the turbine and 0.90 for the drive and generator, and 0.95 × 0.85 × 0.90 = 0.73. Those three numbers are illustrations, not measurements.
A homemade first build is far from that. The Hydro Generator page puts efficiency at 0.25 to 0.50 and recommends 0.3 for a rough estimate. The factor then becomes 9.81 × 0.3 = 2.94, or 9.81 × 0.5 = 4.9 at the top of that range.
Worked Example: The Carrier’s Three Sites Under Two Efficiencies
| Flow | Head | Q × H × 7 | 9.81 × Q × H × 0.3 |
|---|---|---|---|
| 5 L/s | 10 m | 350 W | 147 W |
| 20 L/s | 20 m | 2,800 W | 1,177 W |
| 50 L/s | 50 m | 17,500 W | 7,358 W |
At every row the shortcut is 7 ÷ 2.94 = 2.4 times the homemade figure. Plan a first system on the lower column and treat the upper as the goal after testing. To test, measure Q and H, read the electrical output in watts, and divide: η = P ÷ (9.81 × Q × H).
Energy follows from power and time: 350 W running 24 hours is 350 × 24 = 8,400 Wh, 8.4 kWh per day; 147 W gives 147 × 24 = 3,528 Wh, about 3.5 kWh. Because the stream flows all day, this is the full daily energy, not a peak.
Which Flow Goes Into The Formula
Q is the flow that actually passes through the turbine, not the flow of the stream. Measure the stream in the driest season (Seasonal Variation) and leave part of it in the channel (Tailrace & Environmental Flow). If you can divert 3 of 5 L/s at 10 meters, the shortcut gives 3 × 10 × 7 = 210 watts, not 350.
Hydro is linear; wind is cubic
In this formula doubling the flow doubles the power, and doubling the head doubles the power. Wind power is a different law: P = ½ × ρ × A × v³ × Cp, where ρ is air density, A the swept area, v the wind speed and Cp the fraction of the wind’s power the rotor captures. Doubling the wind speed multiplies the power by 8. Never apply a cube to a stream; never use head or flow for a wind rotor. See Average Wind Speed & Power Curve.
Common Mistakes
- Unit slips — 5 L/s is 300 L/min. Put 300 into the shortcut at 10 m and you get 21,000 watts, sixty times too much.
- Using stream flow instead of turbine flow — the stream’s dry-season flow is not the share you can divert.
- Trusting 7 for an untested build — a measured 0.3 efficiency leaves less than half the figure.
What’s Next
- Learn next: Seasonal Variation for how Q changes over a year
- Combine with: Head Measurement (Elevation Drop) to get H right