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.

Flow Rate (m³/s, e.g., 1):

Gross Head (m, e.g., 100):

Head Loss (m, e.g., 3):

Actual Power Output (W, e.g., 800000 for 800 kW):

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

\\[ h_{\text{net}} = 10 – 0.5 = 9.5 \ \text{m} \\] \\[ P_{\text{theoretical}} = 1000 \cdot 9.81 \cdot 1 \cdot 9.5 = 93,195 \ \text{W} \\] \\[ \eta = \frac{70000}{93195} \approx 0.751 \ \text{(75.1\%)} \\]

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

\\[ h_{\text{net}} = 50 – 3.54 = 46.46 \ \text{m} \\] \\[ P_{\text{theoretical}} = 1000 \cdot 9.81 \cdot 2.265 \cdot 46.46 \approx 1,032,664 \ \text{W} \\] \\[ \eta = \frac{900000}{1032664} \approx 0.871 \ \text{(87.1\%)} \\]

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

\\[ h_{\text{net}} = 100 – 3.30 = 96.70 \ \text{m} \\] \\[ P_{\text{theoretical}} = 1000 \cdot 9.81 \cdot 11.992 \cdot 96.70 \approx 11,380,694 \ \text{W} \\] \\[ \eta = \frac{8000000}{11380694} \approx 0.703 \ \text{(70.3\%)} \\]

Result: Net Head = 96.70 m, Theoretical Power = 11,380,694 W, Efficiency = 0.703 (70.3%)

Formulas Used in Hydropower Turbine Efficiency Calculator

Example Calculations

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