High-Head Hydropower Calculator
High-Head Hydropower Calculator recommends a turbine type (Pelton or Francis) for high-head sites (>50 m) based on net head, flow rate, and desired power, with specific speed calculations and suitability scores.
Formulas Used in High-Head Hydropower Calculator
The calculator uses these formulas to select and evaluate 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 \\]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)
- \\( \eta \\): Turbine efficiency (0 to 1)
- \\( \rho \\): Water density (1000 kg/m³)
- \\( g \\): Gravitational acceleration (9.81 m/s²)
- \\( Q \\): Flow rate (m³/s)
- \\( N_s \\): Specific speed (metric, rpm)
- \\( N \\): Rotational speed (rpm)
Example Calculation
High-Head Site
Input: Gross Head = 200 m, Head Loss = 10 m, Flow Rate = 0.5 m³/s, Rotational Speed = 1500 rpm, Desired Power = 800 kW
\\[
h_{\text{net}} = 200 – 10 = 190 \ \text{m}
\\]
\\[
P = 0.88 \cdot 1000 \cdot 9.81 \cdot 0.5 \cdot 190 / 1000 \approx 820.91 \ \text{kW}
\\]
\\[
N_s = \frac{1500 \sqrt{820.91}}{190^{5/4}} \approx 30.24 \ \text{rpm}
\\]
Pelton (head 50–1000 m, \\( N_s \\) 10–50): Score = 92.
Result: Recommended Turbine = Pelton, Efficiency = 0.85–0.90, Power = 820.91 kW.