capillary-pressure-lifts-a-column - Surface Tension and Capillarity Step by Step

A capillary column is accepted when surface pressure equals column pressure. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Capillary geometry supplies radius and height

The radius controls the upward surface-pressure ledger. The height controls the downward column-pressure ledger.

r=1\ \text{m}\qquad h=1\ \text{m}

Only equal pressures are accepted

The accepted bit is not a judgment word. It is one exactly when the capillary pressure and column pressure match.

\begin{array}{c|c|c|c|c}r&P_{\text{cap}}&h&P_{\text{col}}&\text{accepted}\\1\ \text{m}&20\ \text{Pa}&\tfrac{1}{2}\ \text{m}&10\ \text{Pa}&0\\1\ \text{m}&20\ \text{Pa}&1\ \text{m}&20\ \text{Pa}&1\\1\ \text{m}&20\ \text{Pa}&2\ \text{m}&40\ \text{Pa}&0\\\end{array}

Capillary rise is accepted only when both pressures match

The tube radius and column height are geometry-checked, and the accepted bit follows the pressure equality.

{2\gamma\over r}=2\cdot10\ \text{N/m}/1\ \text{m}=20\ \text{Pa}\quad\text{and}\quad \rho g h=2\ \text{kg}/\text{m}^{3}\cdot10\ \text{m}/\text{s}^{2}\cdot1\ \text{m}=20\ \text{Pa}