Water Network Master Solver
| Topology | Pipe & Node Parameters (Editable) | Pipe Hydraulics | Node Status | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Node | Parent | L (m) | D (mm) | C | Demand (L/s) | Elev (m) | Acc. Flow (L/s) | Velocity (m/s) | Head Loss (m) | HGL (m) | Pressure (m) |
Unlike looped networks, branched (tree) networks are statically determinate. The flow in any pipe is exactly equal to the sum of all downstream nodal demands. The algorithm traverses the tree from the dead-ends back up to the root (Source) to accumulate these flows.
Once flows are known, friction loss ($H_f$) is calculated for each pipe using Hazen-Williams. The Hydraulic Grade Line (HGL) drops sequentially from the source: $HGL_{child} = HGL_{parent} - H_f$.
The ultimate goal of branched network design is ensuring adequate pressure at the taps. Pressure is defined as the available energy head above the physical ground elevation of the node: $Pressure (m) = HGL_{node} - Elevation_{node}$. Minimum residual pressure is typically 15m to 20m of head.
| Pipe Material / Condition | C-Factor |
|---|---|
| PVC, HDPE, Plastic (New) | 140 - 150 |
| Ductile Iron (Cement Lined) | 130 - 140 |
| Commercial Steel / Concrete | 120 - 130 |
| Cast Iron (Old, Corroded) | 80 - 100 |
| Application | Velocity Range |
|---|---|
| Distribution Mains (General) | 0.6 - 1.2 m/s (2 - 4 ft/s) |
| Transmission Mains | 1.0 - 1.5 m/s (3 - 5 ft/s) |
| Max Limit (Water Hammer) | < 3.0 m/s (< 10 ft/s) |
| Min Limit (Prevent settling) | > 0.6 m/s (> 2 ft/s) |
| Pipe | Nodes | Length (m) | Diameter (mm) | True Flow (L/s) | Direction | Velocity (m/s) | Head Loss (m) |
|---|
Unlike manual calculations where the engineer guesses arbitrary flows, this tool mathematically generates an initial spanning tree to guarantee that Continuity ($\sum Q_{in} = \sum Q_{out}$) is perfectly satisfied at every node before iteration begins.
The head loss ($H_f$) in each pipe is determined using the Hazen-Williams equation, where $K$ is the pipe resistance constant.
For a network to be balanced, the net head loss around any closed loop must be zero ($\sum H_f = 0$). If it is not, a flow correction factor ($\Delta Q$) is calculated for each loop and applied to all its pipes. This process repeats until $\Delta Q$ approaches zero.
| Pipe Material / Condition | C-Factor |
|---|---|
| PVC, HDPE, Plastic (New) | 140 - 150 |
| Ductile Iron (Cement Lined) | 130 - 140 |
| Commercial Steel / Concrete | 120 - 130 |
| Cast Iron (Old, Corroded) | 80 - 100 |
| Application | Velocity Range |
|---|---|
| Distribution Mains (General) | 0.6 - 1.2 m/s (2 - 4 ft/s) |
| Transmission Mains | 1.0 - 1.5 m/s (3 - 5 ft/s) |
| Max Limit (Water Hammer) | < 3.0 m/s (< 10 ft/s) |
| Min Limit (Prevent settling) | > 0.6 m/s (> 2 ft/s) |
- Cross, H. (1936). Analysis of flow in networks of conduits or conductors. Bulletin No. 286. University of Illinois Engineering Experiment Station. Google Scholar
- Hazen, A., & Williams, G. S. (1920). Hydraulic Tables: The Elements of Gagings and the Friction of Water Flowing in Pipes (3rd ed.). John Wiley & Sons. Google Scholar
- Walski, P. R., Chase, D. V., Savic, D. A., Watermark, W., & Grayman, D. (2003). Advanced Water Distribution Modeling and Management. Haestad Methods. Google Scholar
- Bhave, P. R. (1991). Analysis of Water Distribution Networks. Technomic Publishing Co. Google Scholar
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