Peristaltic Pump: Lumped-Compliance Flow-Ripple Model

The 3D roller-pump simulator shows the rotor turning; this 2D companion shows the fluid dynamics that turning actually produces. Rather than re-drawing the rotor from another angle, it models the pump as an electrical-analogy circuit: a volumetric flow source Q_in(t) — the steady average flow plus a train of brief "handoff" pulses, one each time a roller engages the tube, n evenly spaced per revolution — feeding a first-order compliance filter that represents the tube and fluid's own elasticity. The filtered output Q_out(t) is integrated in real time and drawn on a live scrolling chart alongside the schematic tube. Because the filter's average gain is exactly 1, its long-run average flow always equals the textbook Q = A·L·RPM/1000 formula regardless of roller count (confirmed numerically to well under 1% error across the whole control range) — but the pulse train's frequency rises with roller count, so more rollers push the ripple further past the filter's corner frequency and it comes out smoother, a mechanism-level account of the pulsation rather than an assumed curve.