Hydropower Flow Duration Curve Calculator
Hydropower Flow Duration Curve Calculator generates a flow duration curve to show the percentage of time a river’s flow rate is equaled or exceeded, aiding hydropower potential assessment, with a detailed breakdown and interactive chart.
Formulas Used in Hydropower Flow Duration Curve Calculator
The calculator uses the following formulas to generate the flow duration curve:
Exceedance Probability:
\\[ P_i = \frac{i}{n + 1} \cdot 100 \\]Flow Duration Curve:
Sort flow rates \\( Q_1, Q_2, \ldots, Q_n \\) in descending order: \\( Q_{(1)} \geq Q_{(2)} \geq \ldots \geq Q_{(n)} \\).
Pair each \\( Q_{(i)} \\) with \\( P_i \\).
Plot \\( Q_{(i)} \\) (y-axis, m³/s) versus \\( P_i \\) (x-axis, %).
Where:
- \\( P_i \\): Exceedance probability for the \\( i \\)-th flow rate (%)
- \\( i \\): Rank of flow rate (1 for highest, 2 for second highest, etc.)
- \\( n \\): Total number of flow rate data points
- \\( Q_{(i)} \\): \\( i \\)-th sorted flow rate (m³/s)
Example Calculations
Example 1: Small Stream (12 Monthly Flows)
Input: Flows = 0.5, 0.7, 0.9, 1.2, 1.5, 1.3, 1.0, 0.8, 0.6, 0.4, 0.3, 0.2 m³/s
Sorted Flows: 1.5, 1.3, 1.2, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2
\\( n = 12 \\), so \\( P_i = \frac{i}{12 + 1} \cdot 100 = \frac{i}{13} \cdot 100 \\)
P1 = \\( \frac{1}{13} \cdot 100 \approx 7.69\% \\), Q1 = 1.5 m³/s
P2 = \\( \frac{2}{13} \cdot 100 \approx 15.38\% \\), Q2 = 1.3 m³/s
…
P12 = \\( \frac{12}{13} \cdot 100 \approx 92.31\% \\), Q12 = 0.2 m³/s
Q10: Flow exceeded 10% of time ≈ 1.3 m³/s (interpolated)
Q50: Flow exceeded 50% of time ≈ 0.8 m³/s (interpolated)
Q90: Flow exceeded 90% of time ≈ 0.2 m³/s (interpolated)
Result: FDC shows flow ranges from 1.5 to 0.2 m³/s; Q10 = 1.3 m³/s, Q50 = 0.8 m³/s, Q90 = 0.2 m³/s
Example 2: Medium River (30 Daily Flows)
Input: Flows = 2.0, 2.5, 3.0, 2.8, 2.3, 1.8, 1.5, 1.2, 1.0, 0.8, 1.1, 1.4, 1.7, 2.1, 2.4, 2.6, 2.9, 3.2, 3.5, 3.1, 2.7, 2.2, 1.9, 1.6, 1.3, 1.0, 0.9, 0.7, 0.6, 0.5 m³/s
Sorted Flows (top 5): 3.5, 3.2, 3.1, 3.0, 2.9, …, (bottom 5): 0.8, 0.7, 0.6, 0.5, 0.4
\\( n = 30 \\), so \\( P_i = \frac{i}{31} \cdot 100 \\)
P1 = \\( \frac{1}{31} \cdot 100 \approx 3.23\% \\), Q1 = 3.5 m³/s
…
P30 = \\( \frac{30}{31} \cdot 100 \approx 96.77\% \\), Q30 = 0.5 m³/s
Q10: Flow exceeded 10% of time ≈ 3.1 m³/s (interpolated)
Q50: Flow exceeded 50% of time ≈ 1.9 m³/s (interpolated)
Q90: Flow exceeded 90% of time ≈ 0.6 m³/s (interpolated)
Result: FDC shows flow ranges from 3.5 to 0.5 m³/s; Q10 = 3.1 m³/s, Q50 = 1.9 m³/s, Q90 = 0.6 m³/s
Example 3: Large River (365 Daily Flows, Summarized)
Input: 365 daily flows ranging from 5.0 to 25.0 m³/s (e.g., sample: 10.2, 12.5, 15.0, …, 8.7)
Sorted Flows (summarized): Max = 25.0, Min = 5.0
\\( n = 365 \\), so \\( P_i = \frac{i}{366} \cdot 100 \\)
Q10: Flow exceeded 10% of time ≈ 20.0 m³/s (interpolated)
Q50: Flow exceeded 50% of time ≈ 12.5 m³/s (interpolated)
Q90: Flow exceeded 90% of time ≈ 6.0 m³/s (interpolated)
Result: FDC shows flow ranges from 25.0 to 5.0 m³/s; Q10 = 20.0 m³/s, Q50 = 12.5 m³/s, Q90 = 6.0 m³/s