Young-Laplace Equation
Calculate capillary pressure via Young-Laplace equation Δp = 2γ·cos(θ)/a and column height with fluid presets and charts for chemistry and physics.
About This Calculator
The Young-Laplace Equation Calculator computes the capillary pressure difference across a curved liquid-gas interface in a thin cylindrical tube, and the equilibrium height of the resulting liquid column. This fundamental equation of surface science and fluid mechanics is essential for students and professionals in chemistry, physics, biomedical engineering, petrochemical engineering, and soil science.
The Young-Laplace equation for a liquid in a thin tube states that the capillary pressure difference Δp across the meniscus is Δp = 2γ·cos(θ)/a, where γ is the surface tension of the liquid (N/m), θ is the contact angle between the liquid and the tube wall (degrees), and a is the inner radius of the tube (mm). The meniscus radius R is first calculated as R = a/cos(θ), then the pressure difference follows from Δp = 2γ/R. At hydrostatic equilibrium, this capillary pressure balances the hydrostatic pressure of the liquid column, giving the column height h = 2γ·cos(θ)/(ρ·g·a), where ρ is the liquid density and g is gravitational acceleration.
Select from built-in fluid presets (pure water, seawater, mercury, ethyl alcohol, benzene, chloroform, glycerine) or choose Custom to enter any surface tension and density. Enter the tube inner radius, contact angle, and optionally override gravitational acceleration and outside pressure. The calculator instantly displays the meniscus radius, capillary pressure in Pa, pressure inside the liquid, and column height in mm, with interactive comparison charts.
Regional Notes
India (IN): Surface tension of water at typical lab temperatures (25°C) is 0.0720 N/m. Standard gravitational acceleration is 9.80665 m/s². The calculator is useful for capillary rise experiments in undergraduate physics and chemistry laboratories across Indian universities.
United States (US): While the calculator uses SI units (Pa, mm, N/m), results can be converted to psi or inches by noting 1 Pa = 0.000145 psi and 1 mm = 0.03937 in. Common contact angles for water on borosilicate glass range from 20° to 40°.
United Kingdom (UK): Standard acceleration due to gravity is 9.80665 m/s² across all regions. The Young-Laplace equation finds extensive application in UK research laboratories working on microfluidics, colloid science, and porous media flow.
Frequently Asked Questions
What is the Young-Laplace equation?
The Young-Laplace equation describes the capillary pressure difference sustained across the interface between two static immiscible fluids due to surface tension. For a liquid in a thin cylindrical tube, it is expressed as Δp = 2γ·cos(θ)/a, where γ is the surface tension, θ is the contact angle, and a is the tube radius.
How do I calculate capillary pressure using the Young-Laplace equation?
Enter the liquid's surface tension (γ), the inner radius of the tube (a), and the contact angle (θ). The calculator computes the meniscus radius R = a/cos(θ) and then the capillary pressure Δp = 2γ/R = 2γ·cos(θ)/a. Results are shown in pascals (Pa).
What is the meniscus radius and why does it matter?
The meniscus radius R is the radius of curvature of the liquid-air interface inside the tube. It equals a/cos(θ), where a is the tube radius and θ is the contact angle. This radius determines the magnitude of the capillary pressure — a smaller meniscus produces a larger pressure difference.
How do I calculate the height of the liquid column in a tube?
At hydrostatic equilibrium, the capillary pressure equals the hydrostatic pressure: ρ·g·h = 2γ·cos(θ)/a. Solving for height gives h = 2γ·cos(θ)/(ρ·g·a), where ρ is the liquid density and g is gravitational acceleration.
What is a contact angle in the Young-Laplace equation?
The contact angle θ is the angle the liquid-air interface makes with the solid surface of the tube wall. Liquids with θ < 90° (like water in glass) are wetting and rise up the tube, producing a concave meniscus. Liquids with θ > 90° (like mercury in glass) are non-wetting and are depressed, producing a convex meniscus.
What fluids are supported by this calculator?
The calculator includes presets for pure water, seawater, mercury, ethyl alcohol, benzene, chloroform, and glycerine with known surface tension and density values at room temperature. You can also select Custom to enter any surface tension and density value for other fluids.
What units does the Young-Laplace equation calculator use?
Surface tension is measured in N/m, tube radius and meniscus radius in mm, density in kg/m³, gravitational acceleration in m/s², pressure in Pa (pascals), and column height in mm. The calculator handles all unit conversions internally.
Where is the Young-Laplace equation applied in real life?
The Young-Laplace equation has widespread applications in soil physics (capillary rise in porous media), petrochemical engineering (hydrocarbon reservoir characterization), biomedical engineering (lung alveoli mechanics), microfluidics (lab-on-a-chip devices), and plant physiology (water transport in xylem vessels).