Buoyancy of Concrete

Concrete isn’t usually considered to be buoyant, although hulls of boats have been made from it. A block of concrete is negatively buoyant, meaning that it will sink. Chicago gangsters in the 20’s used this property of concrete to construct cement overshoes, that would be fitted to a (soon to be) dead person to make the body negatively buoyant for underwater disposal.

The density of concrete varies with its exact composition, but averages around 2,400 kg per cubic meter, or 150lbs per cubic foot. So a cube of concrete 1 foot on each side weighs 150lbs on dry land. We say that this concrete block displaces 1 cubic foot of water. The same volume of sea water weighs 64 pounds, which is the upward buoyant force that is applied to this concrete block when it sits on the bottom of the ocean. The apparent weight of this block will be 86 pounds, which its actual weight of 150lbs (downward force) minus its buoyancy of 64 pounds (upward force). In fresh water, the apparent weight would be a little more, 87.6 pounds, because a cubic foot of fresh water weighs only 62.4 pounds so provides less upward force.

This kind of question is commonly found in the divemaster and instructor exam, although the weight and volume of the object are both given, so you don’t have to worry about density. They’re usually written something like “a concrete block weighing 150 pounds with a displacement of one cubic foot is submerged in sea water, what is the minimum amount of lift required to raise it?”. From the previous paragraph it’s hopefully apparent that the answer is 86 pounds.

Sometimes these questions, posed identically, are about outboard motors. It might be hard to estimate the displacement of an outboard motor as it is a highly irregular shape, which is why the exam questions helpfully provide you with the number. The old story about Archimedes’ problem of measuring the volume of a crown posed the same problem, which he solved by measuring the amount of liquid displaced by the object, and thus its volume. With a large enough graduated cylinder, you could dunk a crown (or an outboard motor) and measure how much the water rises in the cylinder which would be an accurate measure of its volume. Archimedes realized this after overflowing a public bath after getting into it, or so the legend goes.

Concrete blocks on the other hand are often made in nice regular shapes. One familiar example is a pyramidal frustrum, which is simply a pyramid with the top sliced off. A pyramidal frustrum with a square base and a square top is a common shape for buoy anchors. If you call the length of one side of the base b, the length of one side of the top t, and the height of the block h, then the displacement will be ((b+t)/2)² x h. If you make a block that is 2 feet square at the base and 1 foot square at the top and 18 inches high, then using this formula the volume will be 1.5 x1.5×1.5 which equals 3.375 (3 and 3/8) cubic feet. The block will weigh just over 560 pounds, and displace 216 pounds of sea water, so it will appear to weigh 344 pounds under water. Of course, you’ll want to add an iron ring bolt to the top on which to attach a line, and that will add a bit of weight.

If you understand all of the above, you’ll have no trouble with this section of the divemaster or instructor exams.