Try A Little Buoyancy Math!

Buoyancy is governed by something we call Archimedes Principle. It states that

any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body.

The fluids that divers are most concerned with are fresh and salt water. It's necessary to distinguish between the two because equal volumes of the two have different weights. For example, a cubic foot of fresh water weighs approximately 62.4 pounds, but a cubic foot of salt water weighs approximately 64 pounds. Where does the extra weight come from? If you guessed the salt (and a few other minerals), you're right!

Let's Look At An Example:

Let's say you have a solid block that has a volume equal to one cubic foot and weighs 63 pounds. If you put into freshwater, will it sink or float?

We know freshwater has a weight of 62.4 pounds per cubic foot. Our block weighs 63 pounds and displaces 62.4 pounds of water. If we subtract 63 from 62.4 we get -0.6 pounds. This means our block is negatively buoyant and will sink.

What if we place the same object in seawater?

Seawater has an average weight of 64 pounds per cubic foot. Again, our block weighs 63 pounds which is less than the weight of the water displaced. If we do the math we find 63 pounds from 64 pounds gives us 1.0 pounds. Our block is positively buoyant and will float.

Trick Question: If you added one pound of weight to our block and placed it back in the seawater, would it sink or float?

The answer is neither! If we subtract 64 pounds from 64 pounds we get zero pounds. Our block would be neutrally buoyant!

You Try It:

1. Let's use a real-life example. Let's say an Aquarius scientist needed to send a sample of dead coral to the surface to be analyzed. The sample was calculated to weigh roughly 250 pounds and displaces 1.5 cubic foot of water. How big of an airlift bag (in cubic feet) would be required so we could lift this sample to the surface for retrieval?

2. Here's another. Another Aquarius scientists is collecting sediment samples from near the reef. He collects two cubic feet of sediment that weighs approximately 210 pounds. He also needs to send his samples to the surface for retrieval and has several airlift bags that have a volume of approximately one gallon. How many will he need to send his samples to the surface? (hint: one gallon of seawater weighs about 8 pounds)

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Lesson design by Lucas Gillispie.