What is the Darcy-Weisbach equation for pipe friction?

The Darcy-Weisbach equation calculates head loss h_f = f · (L/D) · (v² / 2g) and pressure drop ΔP = f · (L/D) · (ρ·v² / 2), where f is the Darcy friction factor, L is pipe length, D is hydraulic diameter, v is mean fluid velocity, and ρ is fluid density.

How is the friction factor (f) determined?

For laminar flow (Re 4000), f is iteratively solved using the implicit Colebrook-White equation 1/√f = -2.0·log10( (ε/D)/3.7 + 2.51/(Re·√f) ), taking into account relative surface roughness (ε/D).

What is the recommended maximum liquid velocity in piping?

For general water and industrial liquid service, flow velocity is typically kept between 1.0 m/s and 2.5 m/s (3 to 8 ft/s). Velocities above 3.0 m/s (10 ft/s) increase pipe wall erosion, acoustic noise, and water hammer vulnerability.

Fluid Power & Piping

ASME B36.10M / Darcy-Weisbach

PRO Suite

Pipe Flow & Darcy-Weisbach Pressure Drop PRO Calculator

Compute major friction head loss (Darcy-Weisbach), minor fitting losses (ΣK), Colebrook-White friction factor (f), Reynolds number, and required pump shaft power across ASME B36.10M pipe schedules.

Pipe Flow & Darcy-Weisbach Hydraulic Audit

Optimal Velocity

Total Differential Pressure Drop (ΔP_total)

0.412bar

Equivalent Head Loss: 4.21 m fluid column

Mean Flow Velocity (v)

0.23 kW Pump

1.92m/s

Shaft Power required: 0.23 kW

Pipe Friction Loss0.382 barDarcy-Weisbach

Fittings Minor Loss0.031 barValves & Bends

Elevation Head0.000 barStatic lift

Reynolds Number & Colebrook Friction (f)

f = 0.0217

Reynolds Number Re = 100,668

turbulent

Fully turbulent flow profile (Re > 4000). Friction factor governed by pipe wall relative roughness (ε/D) via the Colebrook-White equation.

Laminar (Re < 2300)TransitionTurbulent (Re > 4000)

Darcy Friction (f)0.02166Darcy-Weisbach

Relative Roughness (ε/D)8.571e-4Commercial Carbon Steel (New / Clean)

Flow Sensitivity: ΔP & Velocity vs. Flow Rate

ΔP (bar)

v (m/s)

Hover over points to inspect quadratic pressure drop scaling and pump power requirements across throttling ranges.

Calculation Summary

Input Parameters

Pipe Inner Diameter (D)	52.5mm
Pipe Length (L)	50m
Volumetric Flow Rate (Q)	15m3/h
Fluid Type	Clean Water (20°C / 68°F)
Pipe Wall Material	Commercial Carbon Steel (New / Clean)
Total Minor Loss (ΣK)	1.67

Calculated Results

Mean Flow Velocity (v)	1.92m/s KEY
Reynolds Number (Re)	100,668 KEY
Darcy Friction Factor (f)	0.02166
Total Pressure Drop (ΔP)	0.412bar KEY
Equivalent Total Head (H)	4.21m
Required Pump Shaft Power	0.23kW KEY

Safety Notes

Flow is in TURBULENT regime. Friction calculations follow Colebrook-White implicit formulation with Darcy-Weisbach head loss equations.

Mathematical Models & Equations

Flow Velocity (v)

v = \frac{Q}{A} = \frac{4 Q}{\pi D^2} \quad [\text{m/s or ft/s}]

Reynolds Number (Re)

Re = \frac{\rho \cdot v \cdot D}{\mu} = \frac{v \cdot D}{\nu} \quad (\text{Laminar if } Re < 2300, \text{ Turbulent if } Re > 4000)

Colebrook-White Friction Factor (f)

\frac{1}{\sqrt{f}} = -2.0 \log_{10} \left( \frac{\epsilon / D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \quad (\text{for turbulent flow})

Darcy-Weisbach Major Head Loss (h_f)

h_f = f \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{v^2}{2g}\right) \quad [\text{meters or feet}]

Major Friction Pressure Drop (ΔP_major)

\Delta P_{\text{major}} = f \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{\rho v^2}{2}\right) = \rho g h_f \quad [\text{Pa or bar / psi}]

Minor Fitting Losses (ΔP_minor)

\Delta P_{\text{minor}} = \sum K \cdot \left(\frac{\rho v^2}{2}\right) \quad (K = \text{fitting resistance factor})

Hydraulic Pumping Power (P_pump)

P_{\text{pump}} = \frac{\Delta P_{\text{total}} \cdot Q}{\eta_{\text{pump}}} \quad [\text{kW or HP}]

Verification Calculation Log

1Pipe Internal Geometry & Flow Velocity (v):
- •Pipe Inner Diameter: D = 52.5 mm (2.067 in).
- •Flow Cross-Sectional Area: A = (π/4) · D² = 0.002165 m².
- •Volumetric Flow: Q = 15 m3/h = 15.00 m³/h = 4.167 L/s.
- •Mean Flow Velocity: v = Q / A = 1.925 m/s (6.31 ft/s).
2Fluid Properties & Reynolds Number (Re):
- •Fluid: Clean Water (20°C / 68°F) (Density ρ = 998.2 kg/m³, Dynamic Viscosity μ = 1.002 cP = 1.002e-3 Pa·s).
- •Reynolds Number: Re = (ρ · v · D) / μ = (998.2 × 1.925 × 0.0525) / 1.002e-3 = 100668.
- •Flow Regime: TURBULENT (Fully Turbulent (Re > 4000)).
3Pipe Wall Roughness & Darcy Friction Factor (f):
- •Pipe Material: Commercial Carbon Steel (New / Clean) (Absolute Roughness ε = 0.045 mm).
- •Relative Roughness: ε/D = 0.045 / 52.5 = 0.000857.
- •Colebrook-White Friction Factor: 1/√f = -2.0 log₁₀( (ε/D)/3.7 + 2.51/(Re √f) ) -> f = 0.02166.
4Major Friction Head Loss & Pressure Drop (Darcy-Weisbach):
- •Pipe Length L = 50 m.
- •Dynamic Pressure: q = 0.5 · ρ · v² = 0.5 × 998.2 × (1.925)² = 1849.0 Pa.
- •Major Pressure Drop: ΔP_major = f · (L/D) · q = 0.382 bar (Head loss h_f = 3.90 m).
5Minor Fitting Losses, Elevation Head & Total Differential Pressure:
- •Minor Fitting Loss: ΔP_minor = ΣK · q = 0.031 bar.
- •Total System Pressure Drop: ΔP_total = ΔP_major + ΔP_minor + ΔP_elevation = 0.412 bar (Total Head H = 4.21 m).
6Hydraulic & Shaft Pumping Power (η_pump = 75%):
- •Hydraulic Power: P_hyd = ΔP_total · Q = 0.17 kW.
- •Required Pump Shaft Power: P_shaft = P_hyd / η = 0.23 kW (0.31 HP).

Engineering DisclaimerEngineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.

Pipe Flow & Darcy-Weisbach Pressure Drop PRO Calculator

Pipe Flow & Darcy-Weisbach Hydraulic Audit

Reynolds Number & Colebrook Friction (f)

Flow Sensitivity: ΔP & Velocity vs. Flow Rate

Calculation Summary

Mathematical Models & Equations

Verification Calculation Log

Pipe Flow & Pressure Drop Engineering Report — Calculation Report

Pipe Flow & Pressure Drop Engineering Report

Design Inputs

Calculated Results

Related Calculators

Applicable Standards

Related Formulas

Pipe Flow & Darcy-Weisbach Hydraulic Audit

Reynolds Number & Colebrook Friction (f)

Flow Sensitivity: ΔP & Velocity vs. Flow Rate

Calculation Summary

Mathematical Models & Equations

Verification Calculation Log

Pipe Flow & Pressure Drop Engineering Report — Calculation Report

Pipe Flow & Pressure Drop Engineering Report

Design Inputs

Calculated Results

Related Calculators

Applicable Standards

Related Formulas

Flow Velocity:	1.92 m/s
Reynolds Number:	100668
Darcy Friction Factor:	0.02166
Total Pressure Drop:	0.412 bar
Required Pump Power:	0.23 kW