Advanced pipe flow · calculator
Darcy-Weisbach Friction Factor & Pipe Head Loss Calculator
Calculate Darcy friction factor from Reynolds number and relative roughness, then estimate head loss for a full circular pipe.
Method record
What this calculator measures
Darcy-Weisbach applies dimensional physics across fluids. Friction factor depends on flow regime and, in turbulent flow, pipe relative roughness.
f = 64/Re (laminar); f ≈ 0.25/[log₁₀(ε/3.7D + 5.74/Re⁰·⁹)]² (turbulent) Use it correctly
Calculation steps
- Calculate Reynolds number from fluid conditions.
- Use roughness and diameter in the same unit.
- Apply the resulting Darcy factor to head-loss calculations.
Applicability
Use the model within its limits
The transitional range is not reliably represented by a single steady friction-factor correlation.
What this result represents
- System
- Advanced pipe flow
- Formula
- f = 64/Re (laminar); f ≈ 0.25/[log₁₀(ε/3.7D + 5.74/Re⁰·⁹)]² (turbulent)
- Review
- Verify safety-sensitive work with qualified guidance.
Worked Field Example
Worked Example: Fully Turbulent Pipe Friction Factor
Field Scenario: Calculating the Darcy-Weisbach friction factor for water flowing at 6.5 ft/s through a 6-inch commercial steel pipe at 60°F.
Given Input Parameters
Step-by-Step Mathematical Solution
- Calculate Reynolds Number: Re = (v × D) / ν = (6.5 × 0.5054) / (1.217 × 10^-5) ≈ 269,934 (Fully Turbulent).
- Relative Roughness: ε / D = 0.00015 / 0.5054 ≈ 0.0002968.
- Swamee-Jain formula: f = 0.25 / [log10(ε / 3.7D + 5.74 / Re^0.9)]² = 0.25 / [log10(0.0000802 + 0.0000721)]² = 0.25 / [-3.817]² ≈ 0.01715.
Darcy friction factor f ≈ 0.0172.
Professional Guidance: The Swamee-Jain explicit equation agrees within 1% of the implicit Colebrook-White equation for Re > 4,000.
Engineering FAQs
Frequently Asked Questions
How does Darcy friction factor (f) differ from Fanning friction factor (f_F)?
The Darcy friction factor f is exactly 4 times the Fanning friction factor (f = 4 × f_F). Civil and mechanical engineers typically use Darcy friction (h_f = f × (L/D) × (v²/2g)), while chemical engineers often use Fanning friction.
What is the transition boundary between laminar and turbulent pipe flow?
Flow is laminar when Re < 2,000 (where f = 64 / Re). The flow regime transitions between Re = 2,000 and 4,000, and is considered fully turbulent when Re > 4,000.
Why is Darcy-Weisbach more accurate than Hazen-Williams?
Darcy-Weisbach is theoretically exact and derived from conservation of momentum. It accounts for fluid viscosity, density, and temperature, making it applicable to any liquid or gas, whereas Hazen-Williams is valid only for ambient liquid water.