Formula used
For a circular tube, Jurin’s law is h = 2γ cosθ ÷ (ρgr). The diameter form is h = 4γ cosθ ÷ (ρgd).
For two close vertical plates separated by distance b, the calculator uses h = 2γ cosθ ÷ (ρgb). The annular option applies the same narrow-gap approximation to the radial clearance.
Capillary pressure is estimated from Δp = 2γ cosθ ÷ r. The Bond number is Bo = ρgr² ÷ γ.
Early-time Washburn penetration is estimated using L = √(rγ cosθ·t ÷ 2μ). This relation neglects gravity and inertia.
How to use this calculator
- Select a tube, plate, annular, porous, or Washburn model.
- Choose the liquid and surface presets, then edit their properties when measured data is available.
- Enter the active radius, diameter, gap, or effective pore size with its unit.
- Set contact angle, gravity, temperature, viscosity, and optional corrections.
- Select the required output, then submit the form.
- Review the result, warning messages, comparison tables, charts, and formula substitution.
Worked examples
| Application | Typical input | Expected behavior |
|---|---|---|
| Water in clean glass | γ = 0.072 N/m, ρ = 998 kg/m³, θ = 20°, radius = 0.5 mm | Positive capillary rise with a concave meniscus. |
| Mercury in glass | γ = 0.485 N/m, ρ = 13,546 kg/m³, θ above 90° | Negative height representing capillary depression. |
| Concrete pore estimate | Effective radius = 50 µm, θ = 40°, custom correction factor | Approximate equilibrium moisture rise, limited by pore variability. |
| Ink penetration in paper | Small pore radius, measured viscosity, short time | Washburn length estimates early penetration distance. |
Important assumptions and limitations
The equilibrium models assume static conditions, uniform geometry, constant liquid properties, negligible evaporation, and an open capillary exposed to equal surrounding pressure.
Contact angles depend on surface cleanliness, roughness, contamination, temperature, and measurement direction. Preset values are approximate and should not replace laboratory data.
Porous materials contain distributed pore sizes and connected pathways. Their displayed result is an idealized engineering estimate rather than a complete unsaturated-flow simulation.
Frequently asked questions
What causes capillary rise?
Surface tension and adhesion pull a wetting liquid upward until the liquid-column weight balances the vertical surface force.
Why can the result be negative?
A contact angle above 90 degrees makes cosine negative, indicating capillary depression and a convex meniscus.
Does atmospheric pressure change the ideal result?
Not when both the reservoir and capillary surface experience the same atmosphere. Pressure effects matter in sealed or differentially pressurized systems.
Why does a smaller tube produce a greater rise?
Capillary pressure increases as radius decreases, while the supported liquid volume decreases rapidly.
What is the Bond number?
It compares gravitational effects with surface-tension effects. Small values indicate stronger capillary dominance.
Can this calculate soil moisture rise?
It provides an effective-pore estimate. Real soils need pore distributions, retention curves, and hydraulic conductivity models.
What does the meniscus correction do?
It applies an approximate radius divided by three correction to relate ideal rise to a measurable column reference.
When should Washburn’s equation be used?
Use it for early-time viscous penetration where gravity and inertia are relatively small.
Are preset liquid properties exact?
No. They are approximate reference values and vary with purity, temperature, and data source.
Can I solve backward for tube size?
Yes. Select required radius or diameter and provide the known target height.