Run-of-River Hydropower Calculator

Usable Flow Rate:

\\[ Q_{\text{usable}} = Q_{\text{total}} – Q_{\text{env}} \\]

Flow Velocity:

\\[ v = \frac{Q_{\text{usable}}}{\pi (D/2)^2} \\]

Head Loss:

\\[ h_{\text{loss}} = \left( f \cdot \frac{L}{D} \cdot \frac{v^2}{2g} \right) + \left( K \cdot \frac{v^2}{2g} \right) \\]

Net Head:

\\[ h_{\text{net}} = h_{\text{gross}} – h_{\text{loss}} \\]

Power Output:

\\[ P = \eta_{\text{turbine}} \cdot \eta_{\text{generator}} \cdot \rho \cdot g \cdot h_{\text{net}} \cdot Q_{\text{usable}} \\]

Power in Kilowatts:

\\[ P_{\text{kW}} = \frac{P}{1000} \\]

Turbine Selection:

• Kaplan: Head 2–20 m, Usable Flow > 1 m³/s
• Francis: Head 10–30 m, Usable Flow 0.5–10 m³/s
• Crossflow: Head 2–30 m, Usable Flow < 1 m³/s

Where:

• \\( Q_{\text{usable}} \\): Usable flow rate (m³/s)
• \\( Q_{\text{total}} \\): Total flow rate (m³/s)
• \\( Q_{\text{env}} \\): Environmental flow (m³/s)
• \\( v \\): Flow velocity (m/s)
• \\( D \\): Penstock diameter (m)
• \\( h_{\text{loss}} \\): Head loss (m)
• \\( f \\): Friction factor
• \\( L \\): Penstock length (m)
• \\( K \\): Minor loss coefficient
• \\( g \\): Gravitational acceleration (9.81 m/s²)
• \\( h_{\text{net}} \\): Net head (m)
• \\( h_{\text{gross}} \\): Gross head (m)
• \\( P \\): Power output (W)
• \\( \eta_{\text{turbine}} \\): Turbine efficiency
• \\( \eta_{\text{generator}} \\): Generator efficiency
• \\( \rho \\): Water density (kg/m³)

\\[ Q_{\text{usable}} = 2 – 0.4 = 1.6 \ \text{m³/s} \\] \\[ v = \frac{1.6}{\pi (1/2)^2} \approx 2.04 \ \text{m/s} \\] \\[ h_{\text{loss}} = \left( 0.02 \cdot \frac{150}{1} \cdot \frac{2.04^2}{2 \cdot 9.81} \right) + \left( 0.5 \cdot \frac{2.04^2}{2 \cdot 9.81} \right) \approx 0.84 \ \text{m} \\] \\[ h_{\text{net}} = 8 – 0.84 = 7.16 \ \text{m} \\] \\[ P = 0.85 \cdot 0.90 \cdot 1000 \cdot 9.81 \cdot 7.16 \cdot 1.6 \approx 86005.2 \ \text{W} \\] \\[ P_{\text{kW}} = \frac{86005.2}{1000} \approx 86.01 \ \text{kW} \\]

Turbine: Kaplan (Head 2–20 m, Usable Flow > 1 m³/s)

\\[ Q_{\text{usable}} = 0.6 – 0.2 = 0.4 \ \text{m³/s} \\] \\[ v = \frac{0.4}{\pi (0.4/2)^2} \approx 3.18 \ \text{m/s} \\] \\[ h_{\text{loss}} = \left( 0.03 \cdot \frac{50}{0.4} \cdot \frac{3.18^2}{2 \cdot 9.81} \right) + \left( 0.3 \cdot \frac{3.18^2}{2 \cdot 9.81} \right) \approx 2.08 \ \text{m} \\] \\[ h_{\text{net}} = 4 – 2.08 = 1.92 \ \text{m} \\] \\[ P = 0.75 \cdot 0.85 \cdot 1000 \cdot 9.81 \cdot 1.92 \cdot 0.4 \approx 4802.4 \ \text{W} \\] \\[ P_{\text{kW}} = \frac{4802.4}{1000} \approx 4.80 \ \text{kW} \\]

Turbine: Crossflow (Head 2–30 m, Usable Flow < 1 m³/s)

\\[ Q_{\text{usable}} = 5 – 1 = 4 \ \text{m³/s} \\] \\[ v = \frac{4}{\pi (2/2)^2} \approx 1.27 \ \text{m/s} \\] \\[ h_{\text{loss}} = \left( 0.015 \cdot \frac{200}{2} \cdot \frac{1.27^2}{2 \cdot 9.81} \right) + \left( 0.7 \cdot \frac{1.27^2}{2 \cdot 9.81} \right) \approx 0.27 \ \text{m} \\] \\[ h_{\text{net}} = 15 – 0.27 = 14.73 \ \text{m} \\] \\[ P = 0.80 \cdot 0.92 \cdot 1000 \cdot 9.81 \cdot 14.73 \cdot 4 \approx 424947.7 \ \text{W} \\] \\[ P_{\text{kW}} = \frac{424947.7}{1000} \approx 424.95 \ \text{kW} \\]

Turbine: Kaplan (Head 2–20 m, Usable Flow > 1 m³/s)