Volumes are in m³; flow rates are in L/s and are converted to m³/s inside the balance. Rain capture uses the catchment area and rainfall depth per hour.
The pump-flow relation is an approximate positive-displacement capacity model. Pressure is estimated from hydrostatic head minus an approximate pipe-loss term; it is not a full network solver.
The motor temperature uses the closed-form solution over each fixed step. Pump losses are estimated from hydraulic power and the user-set efficiency.
Water balances advance with a fixed 1/120 s explicit step and an accumulator. The analytic graph is a reference curve assuming the initial pump flow and demand remain constant; it intentionally does not include later events or control changes.
Water is incompressible and has constant density; tank cross-section is treated as constant; the source basin is well mixed; there are no pipe leaks; pump head is approximated as 14 m; the pipe-flow exponent and friction coefficient are tuned for an educational model. The scene is illustrative, not an engineering design tool. All numerical results are approximate.