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Flow Network Calculator

Segment-by-segment hydraulic build-up for a pipe run — friction, fittings, equipment, static head, and a safety factor — with Colebrook friction and Crane K-values.

When to use this calculator

Use when a single pressure-drop number is not enough and you need the whole path added up: a pump discharge route through several changes of size, a header with branches, or a circuit where you need to see which segment is eating the budget. It builds each segment from friction plus fitting K, applies a safety factor to the pipe-and-fitting portion, and adds equipment drops and static head to produce the total the pump must deliver.

Required inputs

  • Per segment: flow, inside diameter, length, roughness, fluid properties
  • Fitting K-values, plus any unrecoverable and other K terms
  • Fixed equipment pressure drops
  • Elevation change ΔZ and a safety factor on the pipe-and-fitting loss

Expected outputs

  • Velocity, Reynolds number, regime, and friction factor per segment
  • ΣK and the split between friction, fittings, equipment, and static head
  • Segment pressure drop and the running total for the path

Formula overview

ΔP in kPa (hence the /1000 and /2000 in the constants), V in m/s, ρ in kg/m³, D and L in m, ΔZ in m.

  ΔP = [(K_f + f·L/D)·(1 + SF) + K_u] · ρV²/2000
     + K_o · ρV²/2000
     + ρ·g·ΔZ / 1000
     + ΔP_fixed

  V  = Q/A       Re = ρVD/μ
  f  = 64/Re laminar, Colebrook–White turbulent

The safety factor SF applies to the pipe and fitting loss only — not to
equipment drops or to static head, which are known quantities.

Worked example

One segment: DN 50, L = 100 m, water at 2 m/s, ρ = 998 kg/m³,
f = 0.0216, fitting ΣK = 2.0, safety factor 10%, ΔZ = 0

ρV²/2   = 1 996 Pa = 1.996 kPa
f·L/D   = 0.0216 × 100 / 0.05 = 43.2
ΔP      = [(2.0 + 43.2) × 1.10] × 1.996
        = 49.7 × 1.996 = 99.2 kPa ≈ 0.99 bar

Friction is 95% of this segment; the fittings add 4% and the safety
factor 9 kPa. Add the next segment and any equipment drop to the total.

Common mistakes

  • Applying the safety factor to everything. A margin on friction covers roughness and correlation uncertainty; a control valve or exchanger drop taken from a datasheet does not need it, and static head is exact — inflating those just over-sizes the pump.
  • Carrying one velocity across a size change. Each segment has its own diameter, velocity, Reynolds number, and friction factor, and ρV²/2 changes with the fourth power of diameter ratio — a segment must not inherit the one before it.
  • Adding static head twice. If the elevation change is already inside the pump TDH calculation, including it again per segment double-counts it.

FAQ

flow network
hydraulic circuit
Colebrook
Crane TP-410
pump sizing

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