Young Laplace Equation Calculator
Our physical chemistry calculator computes young laplace equation accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
delta-P = gamma * (1/R1 + 1/R2)
The Young-Laplace equation gives the pressure difference across a curved interface. gamma is surface tension, R1 and R2 are principal radii of curvature. For spheres: delta-P = 2*gamma/R. For bubbles: delta-P = 4*gamma/R (two surfaces).
Worked Examples
Example 1: Water Droplet Pressure
Problem:Find the excess pressure inside a water droplet of radius 1 mm (surface tension = 0.0728 N/m).
Solution:delta-P = 2 * gamma / R\ndelta-P = 2 * 0.0728 / 0.001\ndelta-P = 145.6 Pa
Result:Excess pressure = 145.6 Pa (about 0.0014 atm)
Example 2: Capillary Rise in Glass Tube
Problem:Water (gamma = 0.0728 N/m, theta = 0) rises in a glass tube of radius 0.5 mm. Find the height.
Solution:h = 2 * 0.0728 * cos(0) / (998 * 9.81 * 0.0005)\nh = 0.1456 / 4.895\nh = 0.02975 m = 29.75 mm
Result:Capillary rise height = 29.75 mm
Frequently Asked Questions
What is the Young-Laplace equation?
The Young-Laplace equation describes the pressure difference across a curved interface between two fluids due to surface tension. The equation is delta-P = gamma * (1/R1 + 1/R2), where gamma is the surface tension and R1 and R2 are the principal radii of curvature. For a sphere, both radii are equal, simplifying to delta-P = 2*gamma/R. This equation is fundamental in understanding capillary action, bubble formation, droplet behavior, and many biological processes like alveolar mechanics in the lungs.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy