Micro Hydro Power Energy Output Calculator
Micro Hydro Power Energy Output Calculator estimates energy output and recommends a turbine type (Kaplan, Francis, Pelton, or Crossflow) for micro hydropower systems (<100 kW, 2–100 m) based on net head, flow rate, and desired power.
Formulas Used in Micro Hydro Power Calculator
The calculator uses these formulas to estimate energy and select turbines:
Net Head:
\\[ h_{\text{net}} = h_{\text{gross}} – h_{\text{loss}} \\]Power Output:
\\[ P = \eta \cdot \rho \cdot g \cdot Q \cdot h_{\text{net}} / 1000 \\]Daily Energy Output:
\\[ E = P \cdot t \\]Specific Speed:
\\[ N_s = \frac{N \sqrt{P}}{h_{\text{net}}^{5/4}} \\]Suitability Score: Based on head and specific speed ranges.
Where:
- \\( h_{\text{net}} \\): Net head (m)
- \\( h_{\text{gross}} \\): Gross head (m)
- \\( h_{\text{loss}} \\): Head loss (m)
- \\( P \\): Power output (kW)
- \\( E \\): Daily energy output (kWh)
- \\( \eta \\): Turbine efficiency (0 to 1)
- \\( \rho \\): Water density (1000 kg/m³)
- \\( g \\): Gravitational acceleration (9.81 m/s²)
- \\( Q \\): Flow rate (m³/s)
- \\( t \\): Operational hours per day (h)
- \\( N_s \\): Specific speed (metric, rpm)
- \\( N \\): Rotational speed (rpm)
Example Calculation
Micro Hydro System
Input: Gross Head = 15 m, Head Loss = 0.5 m, Flow Rate = 0.1 m³/s, Rotational Speed = 1500 rpm, Desired Power = 10 kW, Hours/Day = 24
\\[
h_{\text{net}} = 15 – 0.5 = 14.5 \ \text{m}
\\]
\\[
P = 0.80 \cdot 1000 \cdot 9.81 \cdot 0.1 \cdot 14.5 / 1000 \approx 11.38 \ \text{kW}
\\]
\\[
E = 11.38 \cdot 24 \approx 273.12 \ \text{kWh/day}
\\]
\\[
N_s = \frac{1500 \sqrt{11.38}}{14.5^{5/4}} \approx 170.68 \ \text{rpm}
\\]
Crossflow (head 5–100 m, \\( N_s \\) 20–100): Score = 90.
Result: Recommended Turbine = Crossflow, Efficiency = 0.75–0.85, Power = 11.38 kW, Energy = 273.12 kWh/day.