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# Stokes' law

## noun

*Physics.*

- the law that the force that retards a sphere moving through a viscous fluid is directly proportional to the velocity of the sphere, the radius of the sphere, and the viscosity of the fluid.
- the law that the frequency of luminescence induced by radiation is usually less than the frequency of the radiation.

## Word History and Origins

Origin of Stokes' law^{1}

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## More About Stokes Law

### What is *Stokes’ law*?

*Stokes’ law* is a law in physics that states that the force that resists a sphere’s fall in a viscous fluid is directly proportional to the velocity of the sphere, the radius of the sphere, and the viscosity of the fluid.

If you have studied physics even a little, you might be familiar with the well-known law that every reaction has an equal and opposite reaction. In physics, this law is used to explain forces, those influences that cause objects to move or to slow down and eventually stop. *Stokes’ law* applies this law of physics to spheres falling in fluids.

According to *Stokes’ law*, F=6πrηv. From left to right, the variables in *Stokes’ law* are as follows:

*F*is the drag force. This is the force that is resisting the sphere’s motion and is trying to make it stop.*r*is the radius of the sphere. It is a measurement of the length from the center of the sphere to any point on its surface.*η*(the Greek letter*eta*) is the viscosity of the fluid. In simple terms, viscosity is a measurement of how “thick” a fluid is. For example, honey has a much higher viscosity than water.*v*is the velocity of the sphere. This is a measurement of how fast the sphere is moving. Velocity also takes into account the gravity pulling the sphere down.

So, if you know the radius of the sphere, the velocity of the sphere, and the viscosity of the fluid, you can use *Stokes’ law* to figure out what the force resisting the sphere would be.

### Why is *Stokes’ law* important?

*Stokes’ law* was discovered by, and named after, British physicist Sir George G. Stokes in 1851. Stokes studied viscous fluids extensively and wrote many scientific papers on them throughout his life.

*Stokes’ law* makes several assumptions that affect the accuracy of its calculations. First, it can only be applied to spheres and no other shapes. Second, it assumes the sphere is falling straight down. Third, it assumes the sphere doesn’t create friction as it falls, which would alter the viscosity of the fluid around it. Last, it assumes the fluid is still and doesn’t have waves or turbulence.

Still, *Stokes’ law* can be used for a variety of practical purposes. For example, it can be used in the study of sediments in water, in determining the viscosity of fluids, in studying rain clouds and fog (as some gases, such as water vapor, are also viscous fluids).

### Did you know ... ?

Sir Stokes was actually close friends with another highly influential physicist, Sir William Thomson. Thomson was also known as Lord Kelvin and is the person the Kelvin scale is named after.

### What are real-life examples of *Stokes’ law*?

This video goes into more depth on the math and physics behind *Stokes’ law.*

<iframe loading="lazy" title="YouTube video player" src="https://www.youtube.com/embed/eD9H-2CQ2i0" width="560" height="315" frameborder="0" allowfullscreen="allowfullscreen"></iframe>

*Stokes’ law* is most familiar to physicists, scientists, and students of physics. In particular, a person is more likely to know this law from studying fluids.

To confirm the social-distance rule: If cough droplets are 0.1 mm and ejected at 10 m/s, a quick Stokes law calculation shows that they travel about 2m laterally and settle in about 1s. https://t.co/tJEFXBo0sy (chart courtesy of @DrPascalMeier).

— George Musser (@gmusser) March 30, 2020

If Stokes' law isn't to do with viscosity then I have truly forgotten everything gleaned from three years of university education.

— Andrew Michael (@moneyandmedia) May 12, 2020

### What other words are related to *Stokes’ law*?

### Quiz yourself!

**Which of the following measurements is not used in Stokes’ law?**

A. radius of a sphere

B. pressure of the fluid

C. velocity of a sphere

D. viscosity of the fluid

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