Tidal Power Hydropower Calculator
Tidal Power Hydropower Calculator estimates energy output and recommends a turbine type (Kaplan, Bulb, or Crossflow) for tidal systems (2–20 m) based on tidal range, flow rate, and desired power.
Formulas Used in Tidal Power Hydropower 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}} \\): Tidal range (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
Tidal Power System
Input: Tidal Range = 5 m, Head Loss = 0.2 m, Flow Rate = 10.0 m³/s, Rotational Speed = 1500 rpm, Desired Power = 500 kW, Hours/Day = 12
\\[
h_{\text{net}} = 5 – 0.2 = 4.8 \ \text{m}
\\]
\\[
P = 0.93 \cdot 1000 \cdot 9.81 \cdot 10.0 \cdot 4.8 / 1000 \approx 437.76 \ \text{kW}
\\]
\\[
E = 437.76 \cdot 12 \approx 5253.12 \ \text{kWh/day}
\\]
\\[
N_s = \frac{1500 \sqrt{437.76}}{4.8^{5/4}} \approx 553.45 \ \text{rpm}
\\]
Bulb (head 2–20 m, \\( N_s \\) 300–1000): Score = 95.
Result: Recommended Turbine = Bulb, Efficiency = 0.90–0.95, Power = 437.76 kW, Energy = 5253.12 kWh/day.