How do Ship Float?

Archimedes' Solve The Problem



The Greek Mathematician and inventor Archimedes lived during the 3rd century BC. According to history he was in the bath one day when he discovered the principle of buoyancy which is the reason why huge Greek ships weighing thousands of pounds could float on water. He noticed that as he lowered himself into the bath, the water displaced by his body overflowed the sides and he realised that there was a relationship between his weight and the volume of water displaced.

Archimedes was not thinking about ships at the time, he was on a mission to solve a question that was asked of him by King Hieron II of Syracuse, the home of Archimedes which was a Greek city at the time. The question that the king had asked was about his crown. Was it pure gold or partly silver? Archimedes reasoned that if the crown had any silver in it, it would take up more space than a pure gold crown of the same weight because silver is not as dense as gold. He compared the crown's volume (measured by the amount of water displaced) with the volume of equal weights of gold and then silver, he found the answer. He had to inform his king that the crown was not pure gold.

The Buoyancy Principle

Archimedes continued to do more experiments and came up with a buoyancy principle, that a ship will float when the weight of the water it displaces equals the weight of the ship and anything will float if it is shaped to displace its own weight of water before it reaches the point where it will submerge.

This is kind of a technical way of looking at it. A ship that is launched sinks into the sea until the weight of the water it displaces is equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo.

The Metacenter

Archimedes figured out that the metacenter had to be determined which is a point where an imaginary vertical line (through the center of buoyancy) intersects another imaginary vertical line (through a new centre of buoyancy) created after the ship is displaced, or tilted, in the water.

The center of buoyancy in a floating ship is the point in which all the body parts exactly balance each other and make each other float. In other words, the metacenter remains directly above the center of buoyancy regardless of the tilt of the floating ship. When a ship tilts, one side displaces more water than the other side, and the center of buoyancy moves and is no longer directly under the center of gravity; but regardless of the amount of the tilt, the center of buoyancy remains directly below the metacenter. If the metacenter is above the center of gravity, buoyancy restores stability when the ship tilts. If the metacenter is below the center of gravity, the boat is unstable and capsizes.

Daniel Bernoulli and The Making of The Fluid Equation

Daniel Bernoulli, born in 1700, came from a long line of mathematicians. His father Johann was head of mathematics at Groningen University in the Netherlands. The family was prone to bitter rivalry: something he was to suffer when he became estranged from his father some 30 years later. At the age of five, the Bernoulli family returned home to Basel in Switzerland, so that Johann's wife could be with her ailing father. Some years earlier Johann had applied to become professor of mathematics at Basel University, but this was denied him because his elder brother, Jakob had deliberately schemed to prevent him getting the post. Later Jakob got the professorship. En route to Basel, Johann learned that Jakob had just died of tuberculosis. He later recalled rather shamelessly that " ... I could succeed to my brother's position." He set about lobbying for the vacant position and in less than two months he got his way.Johann tried to map out Daniel's life, selected a wife for him and decided he should be a merchant. Strangely enough, his own father had tried a similar strategy but Johann had resisted - so did Daniel. However, Daniel spent considerable time with his father and learned much about the secrets of the Calculus which Johann had exploited to gain his fame. By the time Daniel was 13, Johann was reconciled to the fact that his son would never be a merchant but absolutely refused to allow him to take up mathematics as a profession as there was little or no money in it. He decreed that Daniel would become a doctor. For the next few years Daniel studied medicine but never gave up his mathematics.

The Discover How to Measure The Blood Presure





Together Bernoulli and Leonard Euler tried to discover more about the flow of fluids. In particular, they wanted to know about the relationship between the speed at which blood flows and its pressure. To investigate this, Daniel experimented by puncturing the wall of a pipe with a small open ended straw and noted that the height to which the fluid rose up the straw was related to fluid's pressure in the pipe.Soon physicians all over Europe were measuring patients blood pressure by sticking point-ended glass tubes directly into their arteries. It was not until about 170 years later, in 1896 that an Italian doctor discovered a less painful method which is still in use today. However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed.

Bernoulli Discoveres The Fluid Equation

Taking his discoveries further, Daniel Bernoulli now returned to his earlier work on Conservation of Energy. It was known that a moving body exchanges its kinetic energy for potential energy when it gains height. Daniel realised that in a similar way, a moving fluid exchanges its kinetic energy for pressure. Mathematically this law is now written:




where p is pressure, rho is the density of the fluid and u is its velocity. A consequence of this law is that if the velocity increases then the pressure falls. This is exploited by the wing of an aeroplane which is designed to create an area of fast flowing air above its surface. The pressure of this area is lower and so the wing is is sucked upward.