29.74
mm
2.974
cm
0.0297
m
291.2
Pa
1
mm
29.74
mm
2.974
cm
0.0297
m
291.2
Pa
1
mm
The Capillary Rise Calculator determines the height to which a liquid rises (or is depressed) inside a narrow tube due to surface tension. Using Jurin's law: $$h = \frac{2\gamma\cos\theta}{\rho g r}$$ where $$\gamma$$ is the surface tension, $$\theta$$ is the contact angle, $$\rho$$ is the fluid density, g is gravitational acceleration, and r is the tube radius.
Capillary action is responsible for water transport in plants, ink moving through paper, wicking in fabrics, moisture migration in soil and concrete, and the operation of heat pipes and microfluidic devices. Understanding capillary rise is fundamental to soil science, material science, biology, and numerous engineering applications.
Capillary rise occurs when the adhesive forces between a liquid and a tube wall exceed the cohesive forces within the liquid. The liquid wets the wall and climbs until the upward surface tension force balances the weight of the raised liquid column.
The surface tension acts along the circumference of the tube at the contact line, pulling upward with a vertical component:
$$F_{\text{up}} = 2\pi r \gamma \cos\theta$$
The weight of the liquid column is:
$$F_{\text{down}} = \rho g (\pi r^2) h$$
Setting these equal and solving for height:
$$h = \frac{2\gamma\cos\theta}{\rho g r}$$
The corresponding capillary pressure (the pressure difference across the curved meniscus) is given by the Young-Laplace equation for a spherical meniscus in a cylindrical tube:
$$\Delta P = \frac{2\gamma\cos\theta}{r}$$
Key behaviors:
In practice, capillary rise is significant when the tube radius is comparable to the capillary length $$\lambda_c = \sqrt{\gamma/(\rho g)}$$, which is about 2.7 mm for water. For tubes much wider than this, capillary effects are negligible.
A positive height means the liquid rises inside the tube (wetting behavior); a negative height means the liquid is depressed (non-wetting behavior). For water in a 0.5 mm radius glass tube, the rise is about 30 mm. The capillary pressure represents the additional pressure inside the meniscus due to curvature. For design purposes, ensure capillary effects are accounted for in microfluidic channels, porous media, and soil moisture analysis.
Inputs
Results
Water (γ = 72.8 mN/m, θ = 0°) in a 0.5 mm radius glass tube rises approximately 29.7 mm with a capillary pressure of 291 Pa.
Inputs
Results
Mercury (γ = 485 mN/m, θ = 140°) in a 1 mm radius glass tube is depressed by about 5.6 mm — it forms a convex meniscus and sits below the external level.
Jurin's law describes the equilibrium height of a liquid in a capillary tube: $$h = \frac{2\gamma\cos\theta}{\rho g r}$$. It states that capillary rise is directly proportional to surface tension and inversely proportional to both tube radius and fluid density. It applies to straight cylindrical tubes with uniform wetting conditions.
Water wets glass (adhesive forces dominate, θ ≈ 0°), so it rises. Mercury does not wet glass (cohesive forces dominate, θ ≈ 140°), so it is depressed. The sign of cos θ determines whether the liquid rises (θ < 90°) or is depressed (θ > 90°).
Capillary rise is inversely proportional to the tube radius: $$h \propto 1/r$$. Halving the radius doubles the rise height. This is why capillary effects are significant only in narrow tubes, porous media, and microscale systems. In wide containers, capillary rise is negligible.
Capillary pressure is the pressure difference across a curved meniscus, given by the Young-Laplace equation: $$\Delta P = 2\gamma\cos\theta / r$$ for a cylindrical tube. It equals $$\rho g h$$, the hydrostatic pressure of the raised (or depressed) liquid column. Capillary pressure drives fluid flow in porous media.
The capillary length $$\lambda_c = \sqrt{\gamma/(\rho g)}$$ is the length scale at which surface tension and gravity are equally important. For water, $$\lambda_c \approx 2.7$$ mm. Phenomena at scales much smaller than $$\lambda_c$$ are dominated by surface tension; at larger scales, gravity dominates.
Plants use capillary action in the xylem vessels (narrow tubes typically 20–200 μm diameter) to help transport water from roots to leaves. Combined with transpiration pull and root pressure, capillary forces contribute to raising water against gravity. In very narrow xylem vessels, capillary rise alone could lift water several meters.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Density Calculator
Fluid Properties Calculators
Pressure Calculator
Fluid Properties Calculators
Hydrostatic Pressure Calculator
Fluid Properties Calculators
Buoyancy Calculator
Fluid Properties Calculators
Buoyant Force Calculator
Fluid Properties Calculators
Fluid Pressure Calculator
Fluid Properties Calculators
