Download Feeling wall tension in an interactive demonstration of Laplace`s law

Adv Physiol Educ 36: 176, 2012;
doi:10.1152/advan.00034.2012.
Illuminations
Feeling wall tension in an interactive demonstration of Laplace’s law
Milorad Letić
Department of Biophysics, School of Medicine, University of Belgrade, Belgrade, Republic of Serbia
Submitted 15 February 2012; accepted in final form 9 April 2012
Address for reprint requests and other correspondence: M. Letić, Institut za
Biofiziku, Medicinski Fakultet, Univerzitet u Beogradu, Višegradska 26/II,
Beograd 11000, Serbia (e-mail: [email protected]).
176
Fig. 1. The balloon used for demonstration. Such balloons with approximate
dimensions as denoted are given to students. The palpable difference between
the narrow and the wide part is easily felt and there is no possibility of
uncertainty.
curvature) are, as we know, inflated to higher pressures; and
2) tennis balls, compared with basketball balls, are softer,
despite their higher pressure, just because they have a much
smaller radius.
Finally, an example from physiology is presented. Students
are asked to recall, from courses of histology and anatomy,
their knowledge and experience concerning wall structures of
blood vessels, in particular, large structural and mechanical
differences between the wall of the aorta and the wall of a
capillary. According to Laplace’s law, such large structural
differences are not due to the higher pressure in the aorta
because the ratio of blood pressures in these vessels is ⬃4:1 but
are due to the enormously greater radius and wall tension of the
aorta (the ratio of radii is ⬃4,000:1).
Several generations of students appreciated this approach to
the issue and understood the significance of Laplace’s law.
GRANTS
The author was supported by Ministry of Education and Science of the
Republic of Serbia Project 175 036.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
AUTHOR CONTRIBUTIONS
M.L. performed experiments; M.L. prepared figures; M.L. drafted manuscript; M.L. approved final version of manuscript.
REFERENCES
1. Haddad H, Brito I. Feeling Laplace. Adv Physiol Educ 35: 97–98, 2011.
2. Mark HH. The role of eye size in its pressure and motility. Clin Ophtalmol
1: 105–109, 2007.
3. Nave CR, Nave BC. Physics for Health Sciences (3rd ed.). Philadelphia,
PA: Saunders, 1985.
4. Silverthorn DU. Using demonstrations to uncover student misconceptions:
the Law of LaPlace. Adv Physol Educ 22: 281–282, 1999.
1043-4046/12 Copyright © 2012 The American Physiological Society
Downloaded from http://advan.physiology.org/ by 10.220.32.247 on May 10, 2017
LAPLACE’S LAW plays a mayor role in explanations of the wall
tension of structures like blood vessels, the bladder, the uterus
in pregnancy, bronchioles, eyeballs, and the behavior of aneurisms or the enlarged heart.
The general relation of Laplace’s law, expressing that the
product of the radius of curvature (r) and pressure (P) is equal
to wall tension (T) (i.e., r ⫻ P ⫽ T), is quite simple, but
students often have difficulties grasping its significance when
applied to the organism.
Various types of demonstrations (1, 4) and illustrations (3)
are used to familiarize students with the concept.
Here, an interactive demonstration of Laplace’s law is described. During the lecture on blood flow and circulation, when
pressure in different parts of the circulation is elaborated, red
balloons, as shown in Fig. 1, are distributed. Students are asked
to tell the difference they feel by palpation between the narrow
and wide part of the balloon. They all say that the narrow part
of the balloon is softer than the wide part. When asked why this
is so, the answer given is “because of different pressures.” The
fact that, for students, the only possible cause of different
softness is a difference in pressure deserves elaboration.
Through everyday experience students know that, while
inflating a bicycle tire or a ball, they can feel the augmentation
of pressure by palpating the tire or the ball. As a result, the
misconception forms that palpation directly gives information
about pressure. However, the quantity that is directly estimated
by palpation is not the pressure but the wall tension. According
to the general relation expressing Laplace’s law (r ⫻ P ⫽ T),
wall tension is proportional to pressure only in the case where
r is constant. Therefore, a change in pressure can be estimated
by palpation only if the radius does not change. This fact is
often neglected. Even in papers dealing with these issues, the
terms “softness” and “pressure” are used interchangeably without underlying the fixed value of diameter (2).
When students holding the balloons are reminded of Pascal’s
law, it becomes immediately clear to them that pressure is the
same throughout the balloon. At this point, Laplace’s law is
introduced. Now they easily conclude that the palpable difference is caused by different wall tensions. The difference in
wall tension can undeniably be felt by palpation when the ratio
of radii in the narrow and wide part of the balloon is ⬃1:10
(Fig. 1).
Two more examples from everyday experience are discussed
to train students in the application of Laplace’s law: 1) bicycle
tires, when palpated, feel softer than automobile tires, yet
bicycle tires, being narrower (i.e., having smaller radii of