Hydropower Turbine Efficiency Calculator
Hydropower Turbine Efficiency Calculator estimates the efficiency of a hydropower turbine by comparing actual power output to the theoretical maximum power available, with a detailed breakdown and step-by-step calculations.
Formulas Used in Hydropower Turbine Efficiency Calculator
The calculator uses the following formulas to estimate turbine efficiency:
Net Head:
\\[ h_{\text{net}} = h_{\text{gross}} – h_{\text{loss}} \\]Theoretical Maximum Power:
\\[ P_{\text{theoretical}} = \rho \cdot g \cdot Q \cdot h_{\text{net}} \\]Turbine Efficiency:
\\[ \eta = \frac{P_{\text{actual}}}{P_{\text{theoretical}}} \\]Where:
- \\( h_{\text{net}} \\): Net head (m)
- \\( h_{\text{gross}} \\): Gross head (m)
- \\( h_{\text{loss}} \\): Head loss (m)
- \\( P_{\text{theoretical}} \\): Theoretical maximum power (W)
- \\( \rho \\): Water density (1000 kg/m³)
- \\( g \\): Gravitational acceleration (9.81 m/s²)
- \\( Q \\): Flow rate (m³/s)
- \\( \eta \\): Turbine efficiency (0 to 1)
- \\( P_{\text{actual}} \\): Actual power output (W)
Example Calculations
Example 1: Small-Scale Turbine
Input: Flow Rate = 1 m³/s, Gross Head = 10 m, Head Loss = 0.5 m, Actual Power = 70,000 W
Result: Net Head = 9.5 m, Theoretical Power = 93,195 W, Efficiency = 0.751 (75.1%)
Example 2: Medium-Scale Turbine
Input: Flow Rate = 2.265 m³/s, Gross Head = 50 m, Head Loss = 3.54 m, Actual Power = 900,000 W
Result: Net Head = 46.46 m, Theoretical Power = 1,032,664 W, Efficiency = 0.871 (87.1%)
Example 3: Large-Scale Turbine
Input: Flow Rate = 11.992 m³/s, Gross Head = 100 m, Head Loss = 3.30 m, Actual Power = 8,000,000 W
Result: Net Head = 96.70 m, Theoretical Power = 11,380,694 W, Efficiency = 0.703 (70.3%)