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More than a thousand years ago, the great physicist and mathematician Archimedes was taking a dip in a bathtub when he noticed that the water level around him rose. He was so amazed by his miraculous realization that he jumped out and ran naked down the street screaming “Eureka! Eureka!” (I have found it! I have found it!).

Fluid displacement

What Archimedes had found is now known as fluid displacement. Our naked friend had observed that his submerged body displaced a volume of the water equal to the volume of his body. This means that, for example, if I submerge one cubic meter block of concrete into a pool (don’t ask how will I will do it), it will displace one cubic meter of fluid. It’s that simple.

Buoyant force

In addition, the guy screaming “Eureka!” also observed that his body felt lighter when submerged in water. After a while, he discovered that there’s a force pushing the object upwards. This phenomenon is now known as buoyancy, which is defined by the following principle: “A force that’s equal to the weight of the displaced fluid”. The formula for buoyancy is F = -pVg, where p is the surrounding fluid’s density, V refers to the volume of surrounding fluid that objects displace, and g represents the gravitational constant.

Simply put, an object will float when you place it in a fluid if and only if the force pushing the object upwards is greater than the gravitational force that pulls the object down. In other words, the object will float as long as it weighs less than that of the displaced fluid. A floating object has positive buoyancy, whereas a sinking object has negative buoyancy.

The volume of the object and the density of the surrounding fluid are the two major factors in determining the magnitude of the buoyant force. If the object has a large volume, then it is more likely to float because it has strong buoyant force. This is why large objects like ships and boats float. Moreover, the denser the fluids are, the greater the buoyant force. This is the reason objects float easier in water, than in oil or air.

Here’s how it works

Suppose that a cube of concrete (which is denser than water) has a weight of 78596 N. As stated earlier, the cube will displace a cubic meter of the water from the pool, which has a weight of 9800 N. So the concrete will in effect be pushed up by 9800 N of water. 78596 N (the concrete’s real weight) - 9800 N (the displaced water that pushes the object upwards) = 68796 N (the concrete’s weight while submerged). This shows that objects become lighter when submerged in water. So don’t be surprised when your girlfriend seems to lose some pounds when you carry her in the pool.

Now, let’s place a cubic meter block of wood in the pool which has a mass of 490 kg and a density of .49 g/cc cm (water density is 1 g/cc). Again, the cube will displace one cubic meter of water. Since the mass of the displaced water is greater than the submerged block of wood, the force that pushes the object upwards is harder than the force pulling it down). The block of wood will therefore float.

Did you know?

Water is only slightly denser than humans. Now you know why we need to submerge many parts of our bodies to float. Due to a lower fat percentage, men are more dense compared to women, so it’s much easier for women to stay afloat than men.

 

© Sciencetips 2008