Pressure Drop in Pipes — Darcy-Weisbach Equation Explained

The Darcy-Weisbach Equation

Pressure drop in straight pipes is calculated using:

ΔP = f × (L/D) × (ρV²/2)

Where:

• f = Darcy friction factor (dimensionless)
• L = Pipe length (m)
• D = Internal diameter (m)
• ρ = Fluid density (kg/m³)
• V = Mean flow velocity (m/s)

Reynolds Number

First, determine the flow regime:

Re = ρVD/μ

• Re < 2300: Laminar — f = 64/Re
• Re > 4000: Turbulent — use Moody chart or Colebrook equation

Haaland Approximation

For turbulent flow, the Haaland equation provides an explicit approximation:

1/√f = -1.8 × log[(ε/D/3.7)^1.11 + 6.9/Re]

Minor Losses

Fittings and valves add pressure drop using K-factors:

ΔP_minor = ΣK × (ρV²/2)

Common K-values:

• 90° elbow: 0.75
• Gate valve (fully open): 0.17
• Globe valve: 6.4