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According to the Encyclopedia Britannica, "[...] any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface for an object partially submerged in a liquid."

The emphasis is mine, and it is that last part that got me thinking about something: What if a body stays afloat on a liquid whose volume is less than that of the object? That seemingly contradicts Archimedes' Principle because the fluid that the body displaces obviously cannot be equivalent to its actual volume; there's not enough liquid.

Take a look at the image* below:

enter image description here

The can has a volume of 350 mL, so it would theoretically displace roughly that much liquid if it were immersed, but this cannot happen because there is only 230 mL of (artificially colored) water. So, how does Archimedes' Principle account for this apparent paradox? Furthermore, why isn't this discussed more often?

(*The source for the picture is an article written in a foreign language, so I won't bother posting it. Interestingly, I could not find a similar setup on websites in English.)

Qmechanic
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Average Joe
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1 Answers1

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"The volume of displaced fluid" doesn't mean the physical volume of fluid that has moved out of the way. (After all, as you say, that doesn't make sense if there's not much fluid.) The phrase actually means the amount of volume that the floating object takes up which is below the fluid's current level.

Since these two definitions coincide most of the time, common sources conflate the two, but the latter is what actually is used, e.g. in a derivation of Archimedes' principle in any physics textbook.

knzhou
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