Free · Energy scenarios
Water-Turbine Power and Annual Receipts
Compare head-based and free-current water-power scenarios, including discharge, mass flow and gross annual electricity receipts.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
discharge ≈ 2.0000000; mass flow ≈ 2000.0000; power ≈ 78.453200; revenue ≈ 18828.768.
Head power = ηρgHQ; free-current power = ½ηρQv²; Q = Av; annual receipts = power (kW) × 24 × operating days × tariff ($/kWh).
Worked example
Enter these known values and leave the other values blank.
- Turbine type
- Head-based installation
- Cross-sectional area
- 2 m²
- Flow velocity
- 1 m/s
- Head
- 10 m
- Water density
- 1000 kg/m³
- Gravitational acceleration
- 9.80665 m/s²
- Efficiency
- 40 %
- Operating days
- 100 /year
- Tariff
- 0.1 USD / kWh
- Flow discharge
- 2 m³ / sec
- Mass flow rate
- 2000 kg / sec
- Power output
- 78.45 kW
- Revenue
- 18828.77 USD / yrs
Assumptions and limitations
- The head-based branch uses effective hydraulic head and positive volumetric discharge. Overall efficiency includes losses; water density and gravity are editable scenario values.
- The two non-head branches use the kinetic energy of an open current. The captured run-of-river choice is therefore explicitly a free-current scenario; real run-of-river plants can instead use hydraulic head.
- For an ideal unconfined current, the extraction coefficient is bounded by 16/27. This ideal bound does not represent the efficiency limit of a head-based dam turbine.
- Annual receipts assume the stated full-power operation for 24 hours on each entered operating day. They are gross electricity receipts, excluding operating and capital costs.
- Cost inputs are scenario values. Currency conversion choices retain the captured exchange snapshot, rather than live exchange rates; enter all costs in one currency for an internally consistent comparison.
- The calculation assumes the entered operating conditions are constant for the stated comparison period. It does not predict weather, site suitability, construction performance, taxes, financing or maintenance.
- Keep known inputs fixed with locks; clear the unknown before solving an inverse. Singularity or insufficient known inputs can leave results incomplete.
Common questions
Are the outputs a site-specific forecast?
No. They apply the stated algebraic model to supplied conditions. A real installation or building needs measured operating data and a broader engineering or cost assessment.
How are currency choices handled?
They use a fixed captured conversion snapshot. They do not retrieve current prices or exchange rates.
References
- US DOE: hydropower head and flow
- US DOE: head-based and kinetic turbines
- US DOE: ideal Betz coefficient
- Calculation definition and unit reference
Bookify adds explicit model-domain checks: Efficiency must be positive and no more than 100% for head-based power or 16/27 for the ideal open-current model. The electricity tariff cannot be negative. Gross electricity receipts cannot be negative.