Pump and pipe balance
Hₚ = H₀ n² [1 − 0.20(Q/Qᵣ)²]
h_f = (fL/D + K) · v²/(2g), where v = Q/A
Hₚ = Hₛᵧₛ + h_f
The solver finds the operating flow with bounded bisection. The pipe model combines Darcy–Weisbach friction and local fitting losses.
Reservoir and energy balance
Aₜ · dh/dt = Qᵢₙ − Qd − Qleak
p = ρgh · P = ρgQH/η
Water is incompressible. Motor speed and pipe flow approach their targets over finite response times. SI units are used internally; pressure is shown in kPa.
Assumptions and honest simplifications
- Single source basin, one equivalent pipe and one receiving reservoir.
- Pump performance curve and motor response are approximate.
- No water hammer, cavitation, air entrainment or spatial pressure field.
- Friction factor stays constant; scripted incidents alter local losses.
- Representative pressure is an indicator, not a network safety certification.
Use this as an educational model, not as engineering operating advice.
Credits: equations follow standard fluid-mechanics relationships; visual assets are procedural.