Capillary Rise (h = 2S cosθ/(ρga))
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h = 2S cosθ/(ρga)
What each symbol means
| Symbol | What it stands for |
|---|---|
| S | Surface tension of the liquid (N/m) |
| a | Inner radius of the capillary tube (m) |
| g | Acceleration due to gravity (m/s²) |
| h | Height of liquid rise (or depression) in the capillary (m) |
| θ | Angle of contact between liquid and tube wall (rad or deg) |
| ρ | Density of the liquid (kg/m³) |
When to use this
For θ < 90° (e.g., water-glass), liquid rises. For θ > 90° (e.g., mercury-glass), liquid depresses (h is negative because cos θ < 0). Derived from balancing pressure difference across curved meniscus with hydrostatic pressure. h ∝ 1/a — narrower tube, greater rise.