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Hydraulic Network Analysis
Solve a piping network for per-pipe flow and velocity and per-node pressure and head, directly from your drawing — the Todini-Pilati gradient method.
Overview
ErgoPlanner can take the piping you have drawn, treat it as a hydraulic network of nodes and links, and solve the steady-state flow distribution. The solver uses the Todini-Pilati Global Gradient Algorithm (GGA) — the same gradient method used by industry-standard network solvers — to find a flow in every pipe and a head/pressure at every node that simultaneously satisfies continuity at the nodes and the head-loss relationship along each pipe. Results are drawn back onto the canvas as an overlay, so you can read flow, velocity and pressure in place.
In this guide you'll learn
- How a network is extracted from your drawing
- What inputs the solver needs (diameters, lengths, roughness, pumps, boundary heads)
- How to run a synchronous solve and read the on-canvas results
- The difference between the synchronous solve and the durable asynchronous run
Estimated Time: 20 minutes Difficulty: Intermediate
Prerequisites
- A signed-in account
- An engineering entitlement (the Professional plan) — hydraulics is gated
- A drawing containing connected pipework with at least one fixed-head (boundary) node
- Pipe sizing data (diameter, length, roughness) and any pump/demand data
How the solver works
The network is a set of nodes (junctions, sources/sinks) joined by links (pipes). The solver finds the flow Q in each link and the head H at each node by iterating the global gradient equations until continuity and energy balance are met. Head loss along a pipe is computed with the Hazen-Williams relationship
h_L = 10.67 × L / (C^1.852 × d^4.871) × Q^1.852(or the Darcy-Weisbach / Swamee-Jain form), with analytic gradients for fast, robust convergence. Pumps are handled at their operating point on the pump curve. The implementation is validated against a published two-loop golden network and cross-checked with a Hardy-Cross oracle plus continuity and loop-energy invariants.
What the network needs
ErgoPlanner's network builder extracts the topology from the drawing and applies sensible defaults where data is missing (noting any assumptions). For an accurate solve, provide:
| Element | Inputs |
|---|---|
| Pipe (link) | Diameter, length, roughness (Hazen-Williams C or absolute roughness) |
| Node | Elevation; demand (draw-off) where applicable |
| Boundary node | A fixed head (e.g. a reservoir level or supply pressure) — at least one is required |
| Pump | Its curve, so the solver can find the operating point |
Workflow
Step 1 — Prepare the drawing
Build (or open) a drawing whose pipework forms a connected network, with at least one node assigned a fixed boundary head so the solution is determinate. Set pipe diameters, lengths and roughness on the connections, and node elevations/demands as needed.
Step 2 — Run the solve
Trigger the hydraulic solve. ErgoPlanner extracts the network from the drawing and submits it to the solver (POST /hydraulics/solve), which returns the solution immediately for typical network sizes.
Step 3 — Read the results overlay
The solution is rendered on the canvas:
- Per-pipe (link): flow and velocity, shown at the pipe midpoint. A velocity band highlights pipes that are within range, marginal, or running too fast, so undersized pipes stand out at a glance.
- Per-node: head and pressure, shown next to each node.
Adjust diameters or demands and re-solve to iterate the design until velocities and pressures are acceptable.
Synchronous solve vs. durable asynchronous run
ErgoPlanner exposes two ways to run the solver:
- Synchronous solve (
POST /hydraulics/solve) — solves the extracted network and returns the result immediately. This is the path that feeds the on-canvas results overlay and is the right choice for interactive design. - Durable asynchronous run (
POST /hydraulics/runs) — queues the solve as a durable job that survives a server restart, intended for long or batch runs. It reuses the same durable run infrastructure as long simulations.
Note on the async path. The durable asynchronous backend is fully implemented and tested (queue, durable run record, restart-safe claim store). However, the web client for the async run is currently deferred — the on-canvas results overlay is fed by the synchronous solve. In practice this means interactive hydraulics works today through the sync path; the durable-run option is available at the API but is not yet wired into the canvas overlay UI.
Use cases
- Pipe-sizing check — Solve an as-drawn network and use the velocity band to find pipes running too fast or too slow, then resize and re-solve.
- Pump operating point — Confirm a pump delivers the intended duty against the system curve by reading the resulting flows and node heads.
- Pressure-availability check — Verify that every draw-off node has adequate head under the design demand pattern.
- Network debugging — Use continuity at nodes and the per-link flows to locate a topology or boundary-condition error before committing the design.
Related Topics
References
- Todini, E. & Pilati, S. — "A gradient algorithm for the analysis of pipe networks" (1988)
- Rossman, L.A. — EPANET 2 Users Manual (USEPA) — network hydraulics
- Swamee, P.K. & Jain, A.K. — "Explicit equations for pipe-flow problems" (1976)