Real Capillary Dynamics

Capillary Rise Overshoots and Settles

Every value in this lesson is rounded to four decimal places from a real physim numerical integration of capillary rise in a narrow tube (scenario examples/capillary-rise-dynamics-underdamped.json, integrator rk4, fixed timestep dt=0.0002 s), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The real column rises straight past its resting band

The simulated meniscus starts at 0.0050 meters and overshoots to 0.0190 meters at t = 0.1166 seconds — well past where it eventually settles — before falling back.

h(0.0000)=0.0050 m → h(0.1166)=0.0190 mh(0.0000)=0.0050\ \mathrm{m}\ \to\ h(0.1166)=0.0190\ \mathrm{m}
Real capillary overshootThe ghost trail traces the real height-vs-time run; the ledger cites the physim start and first-peak rows.t=0.0000 s height=0.0050 mt=0.1166 s height=0.0190 m

A real integrator shows the oscillation shrinking

The next trough at t = 0.2424 seconds reaches 0.0119 meters, and the next peak at t = 0.3642 seconds only reaches 0.0165 meters — the peak-to-trough swing shrinks from 0.0071 to 0.0046 meters, a real damped oscillation settling toward its resting height, not a clean single step like the idealized pressure-balance chapters.

Δha=0.0071 m → Δhb=0.0046 m\Delta h_a=0.0071\ \mathrm{m}\ \to\ \Delta h_b=0.0046\ \mathrm{m}
Real capillary dampingThe same ghost trail; the ledger adds the trough/second-peak rows and both peak-to-trough swings.t=0.0000 s height=0.0050 mt=0.1166 s height=0.0190 mt=0.2424 s height=0.0119 mt=0.3642 s height=0.0165 mfirst swing (peak-trough)=0.0071 msecond swing=0.0046 m (smaller)