The Young-Laplace (Y-L) equation relates the pressure difference across the interface of two fluids (such as air and water) to the curvature of the interface. The pressure rises on crossing a convex interface such as a rain drop and falls on crossing a concave interface such as the meniscus of water in a glass capillary. The relation between surface geometry and pressure difference across the interface provides the key concept in understanding a large collection of phenomena in hydrostatics. Of the many phenomena in hydrostatics that can be explained readily by the application of the Y-L equation, we consider the ones that are of particular interest in the introductory physics courses. These include the differential pressure within soap bubbles and liquid droplets, the rise and fall of liquids in capillaries, and the depth of liquid spills.

1.
D.
Tabor
,
Gases, Liquids, and Solids,
3rd ed. (
Cambridge University Press
,
New York
,
1991
), pp.
284
285
.
2.
J.
Pellicer
,
V.
Garcia-Morales
, and
M. J.
Hernandez
, “
On the demonstration of the Young-Laplace equation in introductory physics courses
,”
Phys. Educ.
35
,
126
129
(
2000
).
3.
F.
Behroozi
,
H. K.
Macomber
,
J. A.
Dostal
,
C. H.
Behroozi
, and
B. K.
Lambert
, “
The profile of a dew drop
,”
Am J. Phys.
64
,
1120
1125
(
Sept.
1996
).
4.
Readers can view the appendix
at TPT Online, http://dx.doi.org/10.1119/5.0045605, under the Supplemental tab.
5.
H. S. M.
Coxeter
,
Introduction to Geometry
, 2nd ed. (
John Wiley & Sons
,
New York
,
1969
), pp.
351
357
.
6.
The surface curvature is defined by the expression ∇ · n, where n is the unit normal. For example, the surface curvature of a sphere of radius r (with ∇ · n expressed in spherical coordinates) is n=1r2r(r2)=2r.For a cylindrical surface of radius r, the surface curvature (with ∇ · n expressed in cylindrical coordinates) is n=1rr(r)=2r.
7.
Cyril
Eisenberg
,
The Science of Soap Films and Soap Bubbles
(
Dover
,
New York
,
1992
), pp.
21
24
.
8.
F.
Behroozi
and
P. S.
Behroozi
, “
Determination of surface tension from measurement of internal pressure of mini soap bubbles
,”
Am J. Phys.
79
,
1089
1093
(
Nov.
2011
).
9.
Ref. 7, pp.
163
167
.
10.
P. G.
de Gennes
,
F.
Brochard-Wyart
, and
D.
Quéré
,
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
(
Springer
,
New York
,
2004
), pp.
35
38
.
11.
F.
Behroozi
, “
The edge profile of liquid spills
,”
Am. J. Phys.
90
,
10
14
(
Jan.
2022
).
12.
F.
Behroozi
, “
Determination of contact angle from the maximum height of enlarged drops on solid surfaces
,”
Am J. Phys.
80
,
284
288
(
2012
).

Supplementary Material

AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.