Water Displacement

Ever since Archimedes exploded out of his bathtub and ran down the street yelling "Eureka" (which means 'I found it') the principles of water displacement and buoyancy have been understood.

In order to determine that the king's crown was indeed made of gold and not silver covered with gold, Archimedes needed two measurements.

When a solid object is immersed in water, it moves the same amount of water that it occupies as a solid object. The space that something occupies is called volume. A bar of gold (gold ingot) equal in weight to the crown was sunk in a shallow tub. Archimedes added water to the tub until it was about to over-flow.

When the gold was carefully removed, the water level fell slightly. Some historians think the water level didn't fall enough to be measured.

If the water level could be measured, Archimedes might have calculated the volume of the gold. Knowing the width and length of the tub he could have determined the volume of gold by this relation:

Volume = length x width x height water fell

But Archimedes didn't need to measure the volume at all!

Next, he placed the crown in the water. If the crown had the same volume, the water would again rise to the brim of the tub. If there was silver in the crown which takes up more space for the same weight, the water would rise to the brim and spill over!

And it did. The gold crafters were caught by a few drops of water!

The weight of an object occupying a given volume is called density. Because gold is more dense than silver, the gold was placed in the tub first. What if gold was less dense than the silver? Could Archimedes still have discovered the truth?

See how you can measure weight, volume and density using a tub of water.

What's This Got To Do With Your Boat?

Water displacement, buoyancy and the density of wood are vital concepts to know and use while building any wooden boat of any size. Your boat will float only if the volume of water, Vw, it displaces is less than that of your boat, Vb. We can write a mathematical expression to model this:

Vw < Vb

Since the boat's weight W is the weight of the water displaced,

Vw = W/p and Vb = W/pb for p the density of water and pb the average density of the boat. Substitute to get,

W/p < W/pb which means p > pb, the density of water must be greater than the average density of the boat.

But when you want to find out if your boat floats, its easiest to start with the weight and find the volume of water displaced. Then find the volume of the boat's hull. If the displacement volume is less, the boat will float.