The Last Drop
Keep a mountain town supplied through a fragile pumping network. Tune the machinery, read the pressure, and choose who gets water when the system is pushed.
The science · model notes & equations
Hydraulic flow
Hₚ = 32 n² − 0.008 Q²hᶠ = (f L / D + K) · v² / (2g)Q ≈ √[(32n² − Hₛ − 8 m) / (0.008 + (fL/D + K)/(2gA²))]Flow is the positive operating point where estimated pump head balances static lift and pipe losses. Friction factor uses laminar 64/Re or the explicit Haaland approximation to Colebrook–White.
Storage & service
dV/dt = Qpump − Qdelivered − QleakV(t + Δt) = clamp[V(t) + Δt · dV/dt, 0, Vmax]Qdelivered = Qd when fill ≥ 22%; otherwise 0Tank capacity is 240 m³. The 22% cut-off is an intentional, simplified low-pressure service threshold. The analytic line assumes frozen controls and constant flow rates during the forecast window.
Assumptions & limits
Water is incompressible at 1,000 kg/m³; dynamic viscosity is approximated as 0.001 Pa·s. The network is a single equivalent pipe. Pump efficiency is an illustrative speed-based estimate, not a manufacturer curve. Weather is visual ambience only. Pressure transients, water hammer, branching networks, cavitation physics and thermal effects are omitted. Values are approximate and intended for learning, not engineering design.