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Hydraulics2D

Flow in Pipes: Systems & Networks - Theory & Concepts - Pipe Network

Series, parallel and branching pipes, resistance formulations, equivalent systems, three-reservoir problems, Hardy Cross and nodal-head network methods, pumps, valves, demands, and hydraulic transients.

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Two-Pipe System Solver

Uses Darcy–Weisbach major loss plus lumped minor losses:hL=(fL/D+K)V2/(2g)h_L=\left(fL/D+\sum K\right)V^2/(2g).

Pipe 1

Pipe 2

Results

Pipe 1 flow
50.00 L/s
V₁ = 2.83 m/s
Pipe 2 flow
50.00 L/s
V₂ = 2.83 m/s
Pipe 1 head loss
5.848 m
Pipe 2 head loss
5.848 m
Common branch head loss
5.848 m
Continuity residual
0.0e+0 m³/s
Parallel energy residual
0.0e+0 m

The friction factors are user-supplied Darcy factors and are treated as constant. In a full design iteration they must be recomputed from Reynolds number and roughness as flow changes. Pumps, valves with control laws, and elevation differences require the full energy equation rather than this two-branch resistance model.