Cross-section, pump-down curve and flow regime.
The science
Pump-down law. A pump with effective speed S (m3/s) removes gas from a vessel of volume V. With a constant floor pressure p_inf (leaks and outgassing balanced by the pump) V dp/dt = -S (p - p_inf), so p(t) = p_inf + (p_0 - p_inf) exp(-S t / V). The time constant is tau = V / S; every tau the excess pressure drops by 1/e (one decade per 2.30 tau). The throughput is Q = S (p - p_inf). The page integrates the same equation with RK4 and compares.
Mean free path. lambda = k_B T / (sqrt(2) pi d^2 p), with d = 0.365 nm for nitrogen. At atmospheric pressure lambda is about 66 nm; at 1 Pa about 6.6 mm; at 1e-3 Pa about 6.6 m. The Knudsen number Kn = lambda / D (D = vessel diameter) sorts the flow regime: Kn < 0.01 viscous, 0.01 to 0.5 transitional, above 0.5 molecular. In the molecular regime particles hit walls, not each other, and the particle animation switches from collisions to straight flights.
Honest simplifications: a single constant pump speed and constant floor pressure (real pumps have speed curves, staged roughing/turbomolecular trains and the floor changes with outgassing, water vapour and temperature); one gas species; illustrative exhibit numbers, not equipment ratings; particle counts on screen are a visual sample, not a true count.