Fluids A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or liquid. Fluids are able to flow because their particles can move past each other easily. The properties of fluids allow huge ships to float, divers to explore the ocean depths, and jumbo jets to soar across the skies.

Buoyant Force Buoyant force is the upward force exerted on an object immersed in or floating on a fluid. Buoyancy explains why objects float. All fluids exert pressure: the amount of force exerted per unit area of a surface. Archimedes’ principle states that the buoyant force on an object in a fluid is an upward force equal to the weight of the volume of fluid that the object displaces.

A little history… In the first century BC, the Roman architect Vitruvius related a story of how Archimedes, the Greek scientist, discovered that a goldsmith had tried to cheat King Hiero II… The king had given the goldsmith a particular amount of gold to melt down and make into a crown. When the crown was made and returned to the king, the king was suspicious that the goldsmith had stolen some of the gold and replaced it with an equal weight of silver. The king turned to Archimedes for help…

In Vitruvius’s own words: "[Archimedes] happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for he, as he ran, shouted repeatedly in Greek, ‘Eureka, Eureka.’ meaning ‘I have found (it), I have found (it)’.”

He realized that if the bath were completely filled in the beginning, the volume of water that would Overflow would have to be equal to the volume of the person or object Placed into the water!! He now had a way to measure the volume of the irregularly-shaped crown… He discovered that the crown displaced more water than a chunk of gold of equal weight did. Its volume was greater because it contained some silver, a metal less dense than gold!!

Archimedes’ Principle The magnitude of the buoyant force is given by Archimedes’ Principle. It states that… A body fully or partially submerged in a fluid is “buoyed up” by a force that is equal to the _______ of the ___________________. weight displaced fluid D = density of the displaced fluid

DENSITY The Density of an object is defined by the closeness of the molecules present in its structure. Density of water = 1.0 g/ml

An Example:

Objects that Float: Objects that Sink: So… 0 Weight object = F b =Weight displaced fluid > >

?? Density boat > Density water ??

How do boats/ships float? Obviously the density of a metal rowboat or a “concrete canoe” is greater than the density of water, but they float because they contain a large amount of empty space. Because of their _______, they displace enough water to balance their own weight. shape

Cross-Sections of a canoe floating in water: Weight of canoe = ___________________ Weight of canoe plus occupants = ___________________ Canoe is just on the verge of sinking! weight of displaced fluid (shaded in red) weight of displaced fluid (maximum possible shaded in red)

How much water is actually needed to float a ship? Not as much as you’d think!!!... Imagine that the canal is filled with water, and then the ship is slowly lowered into the canal. If the shape of the canal exactly matches the ship, and if the canal is slightly larger than the ship, then all but a thin layer of water all the way around will be displaced. So…. this thin layer between the ship and the canal is really all that is necessary!!

Water Bridge in Germany

Six years to build it, 500 million euros later, and 918 meters long..... This is a channel-bridge over the River Elbe and joins the former East and West Germany, as part of the unification project. It is located in the city of Magdeburg, near Berlin. The photo was taken on the day of inauguration. Did this bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water?

Answer: It only needs to be designed to withstand the weight of the water! Why? A ship always displaces an amount of water that weighs the same as the ship, regardless of how heavily a ship may be loaded.

April News- Gazette Article