Every time this page loads, the solver is checked against analytic solutions right here in your browser. The source code is public on GitHub.
Sizing a cooling-water line, estimating how flow splits after a branch, finding a pump's operating point — most of the questions you want answered before running 3D CFD are piping-network (fluid circuit) calculations. This tool is a 1D piping network solver: wire pipes, valves, pumps and flow sources like a circuit schematic, and every node pressure and element flow rate is computed instantly.
A piping network shares its mathematical structure with an electrical circuit. The one difference is that the resistances are nonlinear (losses scale roughly with flow squared), which is why the system is solved with Newton's method.
| Quantity | Electrical circuit | Piping network |
|---|---|---|
| Across variable (potential) | Voltage V [V] | Pressure ΔP [Pa] |
| Through variable (flow) | Current I [A] | Flow rate Q [m³/s] |
| Resistive element | R [Ω] (linear) | Pipe resistance (nonlinear, ~Q²) |
| Sources | Voltage / current source | Pump / flow source |
Pressure drop in a straight pipe follows the Darcy–Weisbach equation:
ΔP = f · (L/D) · (ρ/2) · v|v|
The friction factor f switches on Reynolds number Re = ρ|v|D/μ. Laminar flow (Re < 2300) uses f = 64/Re — in which case ΔP reduces to the Hagen–Poiseuille solution ΔP = 128μLQ/(πD⁴) — and turbulent flow uses the explicit Swamee–Jain correlation:
f = 0.25 / [log₁₀( ε/(3.7D) + 5.74/Re0.9 )]²
The transition band (Re 2300–3500) is blended so the pressure-drop curve stays continuous. Local losses (valves, bends) follow ΔP = ζ·(ρ/2)·v|v|. Volume conservation — the analogue of Kirchhoff's current law — is enforced at every node and the resulting nonlinear system is solved with Newton's method. The UI displays pressures in kPa and flows in L/min (SI internally).
| Component | Law | Typical use |
|---|---|---|
| Pipe | Darcy–Weisbach (auto laminar/turbulent) | Friction losses in piping |
| Local loss (valve) | ΔP = ζ·(ρ/2)·v² | Valves, bends, fittings, orifices |
| Pump (fixed Δp) | ΔP = constant (ideal source) | Driving a circulation loop |
| Flow source | Q = constant | Imposing a known flow |
| Fixed pressure | — | Tanks, open ends, reference pressure |
This tool solves steady, incompressible, single-phase piping networks. It does not model water hammer, cavitation, two-phase flow, compressible flow or temperature effects. The pump is an ideal fixed-Δp source — real Q-H curves are planned for v0.3. And being 1D it cannot show velocity profiles or vortices; when you need those, move on to the fluid dynamics articles and CFD.
This is v0.2 beta. On the roadmap: pump performance curves, coupling with the thermal network (cooling loops), and transient analysis. Requests are welcome via the request form.