# Law of Laplace

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#### Content Reviewers:

Yifan Xiao, MD#### Contributors:

Salma Ladhani, MD, Evan Debevec-McKenneyThe law of Laplace, named in honor of French scholar Pierre Simon Laplace, is a law in physics that states that the tension in the walls of a hollow sphere or cylinder is dependent on the pressure of its contents and its radius.

The concept was then later applied to medicine since there are many hollow spherical and cylindrical shaped organs in our bodies that deal with pressures.

Important examples include the blood vessels and the chambers of the heart.

Okay, so according to the law of Laplace, wall tension is proportional to pressure (P) times radius (r).

Now, let's break it down.

The wall tension is the force in the container’s walls that resists the force trying to expand it.

So if we’re blowing up a balloon, we can think of the wall tension as the force created by the elastic rubber wall that resists the outward force applied by the pressure inside the balloon.

Now if we break the wall tension into components, we have a vertical vector of force that’s counteracting the expansion of the balloon and a horizontal vector of force that’s stretching and tearing the balloon’s wall.

So, for pressure, if we were to blow more air into a balloon, we would expect the pressure inside to build up and the wall tension of the balloon would increase as the walls push back against the expansion.

If the pressure trying to expand the balloon is greater than the wall tension, the balloon will expand... or pop!

Now another factor is the radius.

A smaller radius means more pressure is needed to overcome the wall tension in order for the container to expand.

This is why it’s harder to blow up a small, deflated balloon than it is to blow up a half inflated balloon.

An example of this can be seen in the alveoli in the lungs of a newborn.

Let’s plug in some easy, imaginary numbers and forego units to make this concept easier to understand!

Normally, an unused alveolus in a newborn is collapsed, so let’s say it has a radius of 2, and the wall tension is 8.

The baby starts crying and inhales.

The pressure of the inhaled air in the alveolus is 4.

So our equation is 4 * 2 which gives us 8, and since this is the same as the wall pressure, the alveolus doesn’t expand.

- "Medical Physiology" Elsevier (2016)
- "Physiology" Elsevier (2017)
- "Human Anatomy & Physiology" Pearson (2017)
- "Principles of Anatomy and Physiology" Wiley (2014)
- "Microcirculation: Mechanics of Blood Flow in Capillaries" Annual Review of Fluid Mechanics (1971)
- "Measuring Wall Shear Stress Using Velocity-Encoded MRI" Current Cardiovascular Imaging Reports (2014)