Darcy-Weisbach Equation

The fundamental equation for pressure drop due to friction in a pipe:

• f — Darcy friction factor (dimensionless)
• L — pipe length (m)
• D — pipe inner diameter (m)
• ρ — fluid density (kg/m³)
• v — mean flow velocity (m/s)

Colebrook-White Equation (Turbulent Flow)

For turbulent flow (Re > 4000), the friction factor is found iteratively:

This calculator uses the iterative Newton-Raphson method (50 iterations) for accurate results matching the Moody diagram.

Laminar Flow

For Re < 2300 (laminar flow), the friction factor is simply:

Minor Losses

Fittings, valves, elbows, and other components add additional pressure drop expressed via K-factors:

Fitting	K-factor	Fitting	K-factor
90° elbow (standard)	0.9	45° elbow	0.4
Tee (through)	0.4	Tee (branch)	1.8
Gate valve (full open)	0.15	Ball valve (full open)	0.05
Check valve (swing)	2.5	Globe valve (full open)	10
Pipe entrance (sharp)	0.5	Pipe exit	1.0
Sudden expansion	~1.0	Sudden contraction	~0.5

Pipe Roughness Values

Material	Roughness ε (mm)	Notes
Carbon steel	0.045	New commercial pipe
Stainless steel	0.015	Smooth welded
Copper	0.0015	Drawn tubing
Plastic (PE, PVC)	0.0015	Very smooth
Cast iron	0.25	New; aged can be 1–3 mm
Hydraulic hose	0.005	Rubber inner liner
Concrete	0.3 – 3.0	Depends on finish

Practical Example