by Earl King

Created on: May 18, 2008

WHAT KEEPS A SHIP AFLOAT

Prior to the late 19th century, anyone could answer the question, "What keeps a ship afloat?". It's made of wood and wood floats. Later toward the end of the century, iron and then steel became the construction material of choice for large ships and battle ships.

I think the answer to the question given above was first given by the Greek Archimedes's (287 212 BC). According to him, "a body wholly or partly submerged in a fluid receives an upward force equal to the weight of fluid displaced". But don't believe me or Archimedes either. Prove it to yourself and do the math.

We must first gather a few facts from the science of hydrostatics.
1. In any liquid pressure exists at every point.
2. The pressure due to the weight of a column of liquid of cross-section A is equal to the depth below the surface times the weight-density (weight per unit volume) of the liquid.
3. Anywhere in a liquid the amount of force due to pressure on a surface is the same regardless of the positioning of the surface and is perpendicular to the surface.

If an object is submerged in a liquid, the horizontal forces will be balanced all around. Otherwise there would be movement.

h = height of object submerged below the surface
DB= depth to bottom of object
DT = depth to top of object
A = area of top or bottom of object
D = weight density (weight per unit vol)
FU= upward force on the bottom of object
FD= downward force on the top of object
B = buoyant force

B = (upward force) (downward force)
B = FU FD = (A x D x DB ) (A x D x DT) = (A x D) {DB DT)

h = DB - DT

Therefore the buoyant force = A x D x h

The last statement indicates that the volume of liquid displaced by the object times the weight density of the liquid will give us the amount of force upward on the object or ship. The ship will therefore float if the upward force equals the total weight of the ship and its contents.

As an outgrowth of this discovery he developed and used the concept of specie gravity. The king had suspected a local goldsmith of cheating him when the man crafted a gold crown. Using this discovery and the specific gravity concept he was able to show that the crown contained a lot of silver.

You may remember that Archimedes made this discovery while in the public baths. He was so overcome, that he jumped out of the water and ran down the street naked shouting eureka, eureka. At least that was the story.

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