Series Pipe Network Calculator

Calculate head losses and velocities in two pipes connected in series using the Darcy-Weisbach equation.

Pipe Networks · Series

Fluid Presets

Diameter unit:

Pipe 1

Length L₁ (m)

Diameter D₁ (mm)

Roughness ε₁ (m)

Pipe 2

Length L₂ (m)

Diameter D₂ (mm)

Roughness ε₂ (m)

Flow Conditions

Flow rate Q (L/s)

Fluid density ρ (kg/m³)

Dynamic viscosity μ (Pa·s)

Q = 10 L/s = 0.010000 m³/s

Theory

Series Network Principles

Q₁ = Q₂ = Q (continuity — same flow everywhere)

hf,total = hf₁ + hf₂ (head losses add in series)

Darcy-Weisbach Equation

hf = f × (L/D) × V²/(2g)

V = Q / A = Q / (π D²/4)

Re = ρ V D / μ

Friction Factor

Laminar (Re < 2300): f = 64/Re

Turbulent (Re ≥ 2300): Swamee-Jain approximation to Colebrook-White

Typical Pipe Roughness

Material	ε (m)	ε (mm)
PVC / drawn tubing	1.5×10⁻⁶	0.0015
Commercial steel	4.6×10⁻⁵	0.046
Galvanized steel	1.5×10⁻⁴	0.15
Cast iron	2.6×10⁻⁴	0.26
Concrete	1×10⁻³	1.0

Because head loss scales with V² and V = Q/A ∝ 1/D², a small reduction in pipe diameter causes a dramatic increase in head loss. Replacing the narrower pipe is usually the most effective upgrade in a series system.