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https://en.wikipedia.org/wiki/Archimedes%27_principle

The wikipedia entry for Archimedes' principle (buoyant force = weight of fluid displaced) has interesting formulas explaining why it's true, but is there an intuitive explanation?

Qmechanic
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Hank Igoe
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2 Answers2

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The intuitive explanation to is: Consider an ideal fluid in equilibrium, now all small sections of this fluid are at rest at all times, this implies the all the forces on any small section balance each other out.

Now let's say you take out a part of the fluid from the top which is of any random shape this segment was at rest earlier , this means the upward force on it by the liquid beneath is equal to the weight of part we took out of the fluid!

Eureka!

When you place an object on the surface on or even inside a fluid and it goes into a place where earlier there was fluid now the fluid below remains unchanged and applies the same force on the object placed

and that force my friend is as explained previously equal to the weight of the liquid we displaced!

user14812745
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  • This is quite intuitive, but there is a mistake. The upward force by the fluid beneath an arbitrary volume is not equal to the weight we took out. That should be the upward force exerted by the entire fluid (a ball rising out of the water starts acceleraring faster once it hits the surface, where there is air above it instead of water). – TBissinger Jan 02 '21 at 09:55
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    Also, the wording is a bit misleading in your fourth paragraph (after the Eureka, which is a nice touch ;) ). It would seem clearer to me if you said: "If you fill the shape you just took out with any object, it feels the same force from the fluid as the fluid that was originally in that place, since nothing changed about the surrounding fluid." Or something along those lines. – TBissinger Jan 02 '21 at 10:00
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The value of buoyant force is given by

$$F = \rho V g$$

(the weight of the displaced fluid). We also know that pressure

$$P = \frac{F}{A}$$

where $P$ is the pressure on the submerged (part of) object and $A$ the area of the same. Now the reason I bring up pressure, is because understanding how pressure affects a submerged object can help you understand buoyancy.

Now the reason behind buoyancy lies in the fact that pressure changes as a function of depth according to the equation

$$P = \rho g h$$

As you can see pressure increases as depth $h$ increases. The area of the object which is at a greater depth, and therefore subject to a greater hydrostatic pressure, will be pushed upwards, towards a lower depth and therefore lower hydrostatic pressure. Think of the fluid as several layers sitting on top of each other with pressure increasing the further down you go.

The same principle applies to say a helium balloon. The pressure of the air beneath the balloon is slightly greater than the pressure above the balloon which results in it floating.

joseph h
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