Formulas

The Penstock Loss Calculator uses the Darcy-Weisbach equation to estimate head loss due to friction:

• Head Loss (\( h_f \)) = \( f \times \frac{L}{D} \times \frac{v^2}{2g} \)
• Where:
  • \( f \) = Friction factor (dimensionless)
  • \( L \) = Length of penstock (meters)
  • \( D \) = Diameter of penstock (meters)
  • \( v \) = Velocity of water (m/s), calculated as \( v = \frac{4Q}{\pi D^2} \)
  • \( Q \) = Flow rate (m³/s)
  • \( g \) = Acceleration due to gravity (9.81 m/s²)

How to Use

1. Enter the penstock length (in meters) in the “Penstock Length” field.
2. Enter the diameter (in meters) in the “Diameter” field.
3. Enter the flow rate (in m³/s) in the “Flow Rate” field.
4. Enter the friction factor (dimensionless) in the “Friction Factor” field.
5. Optionally, click an adjust button to set typical values (e.g., Short Length).
6. Click “Calculate Loss” to see the estimated head loss.
7. Scroll to the “Results” section for details.

Examples

1. Example 1: Length = 500m, Diameter = 0.5m, Flow Rate = 0.5 m³/s, Friction Factor = 0.02
   Head Loss ≈ 0.02 × (500 / 0.5) × (1.273² / (2 × 9.81)) ≈ 1.65m
2. Example 2: Length = 1000m, Diameter = 0.3m, Flow Rate = 0.2 m³/s, Friction Factor = 0.03
   Head Loss ≈ 0.03 × (1000 / 0.3) × (2.827² / (2 × 9.81)) ≈ 12.28m
3. Example 3: Length = 200m, Diameter = 1m, Flow Rate = 2 m³/s, Friction Factor = 0.015
   Head Loss ≈ 0.015 × (200 / 1) × (2.546² / (2 × 9.81)) ≈ 1.00m