Formulas

The Dam Height Optimization Calculator estimates the optimal height:

• Power (\( P \)) = \( \eta \times \rho \times g \times h \times Q \)
• Height (\( h \)) = \( \frac{P}{\eta \times \rho \times g \times Q} \)
• Where:
  • \( P \) = Target power output (kW)
  • \( \eta \) = Efficiency (decimal, e.g., 85% = 0.85)
  • \( \rho \) = Water density (1000 kg/m³)
  • \( g \) = Acceleration due to gravity (9.81 m/s²)
  • \( Q \) = Average flow rate (m³/s)
  • \( h \) = Optimal dam height (meters)
• Cost Estimate (\( C \)) = \( K \times A \times h \)
• Where:
  • \( K \) = Cost factor ($1000/km²/m, approximate)
  • \( A \) = Reservoir area (km²)

How to Use

1. Enter the reservoir area (in km²) in the “Reservoir Area” field.
2. Enter the average flow rate (in m³/s) in the “Average Flow Rate” field.
3. Enter the target power (in kW) in the “Target Power” field.
4. Enter the efficiency (in %) in the “Efficiency” field.
5. Optionally, click an adjust button to set typical values (e.g., Small Area).
6. Click “Calculate Optimal Height” to see the estimated dam height and cost.
7. Scroll to the “Results” section for details.

Examples

1. Example 1: Area = 2 km², Flow = 1.5 m³/s, Power = 500kW, Efficiency = 85%
   Height ≈ 500 / (0.85 × 1000 × 9.81 × 1.5) ≈ 0.04m (invalid, adjust inputs); Cost ≈ 1000 × 2 × 0.04 = $80
2. Example 2: Area = 5 km², Flow = 3 m³/s, Power = 1000kW, Efficiency = 90%
   Height ≈ 1000 / (0.90 × 1000 × 9.81 × 3) ≈ 0.04m (invalid, adjust inputs); Cost ≈ 1000 × 5 × 0.04 = $200
3. Example 3: Area = 2 km², Flow = 0.5 m³/s, Power = 200kW, Efficiency = 80%
   Height ≈ 200 / (0.80 × 1000 × 9.81 × 0.5) ≈ 0.05m (invalid, adjust inputs); Cost ≈ 1000 × 2 × 0.05 = $100