A while back I saw a relatively clever riddle going around that went something like this:
You are in a rowboat in a swimming pool with a 500-lb brick in the boat with you; if you throw the brick out of the boat and into the pool, does the water level in the pool go up, go down, or stay the same?
The answer to this riddle is, rather paradoxically, that the water level goes down. Upon first consideration this doesn’t seem right. You might first think that the brick in the pool will displace water and thus the water level should rise, but then you might remember that the brick was already displacing water in the boat (a boat displaces enough water to equal its total weight and keep it afloat) and think that the water level would stay the same. Neither of these is correct and here’s why.
The brick is more dense than water, hence it sinks in the pool, but what does that really mean? That means that the same volume of water would weigh less than the same volume of brick. Thus, when you are floating the brick at the surface in the boat it displaces an equivalent weight of water, which is a greater volume than the brick itself. I’ll dive deeper into the math (pun totally intended), if anyone cares to read on.
In the illustration above (I have mad Paint skillz) you see that the boat on the left must displace an equivalent volume of water to float its weight and the weight of the brick. On the right the brick is displacing a volume of water equal to its volume and the boat is now only displacing a volume of water equivalent to its own weight.
So, on the left the volume of water that the boat and the brick are displacing can be calculated by adding the weight of the boat and the weight of the brick and dividing the result by the density of water (about 62-lbs per cubic foot). If we say that the boat weighs 120-lbs (for no particular reason) and the brick weighs 500-lbs, then the result is 620/62 or about 10-cubic feet of water being displaced.
On the right, to find the volume of water displaced we would divide the weight of the boat by the density of water, but the volume being displaced by the brick would be its actual volume, which is calculated by dividing its weight by the density of bricks (say 120-lbs per cubic foot). You then add these two volumes together to get the total displacement, and that results in 120/62 + 500/120, or 1.9 + 4.2, or 6.1-cubic feet.
Obviously, 6.1 is less than 10, so the volume of water being displaced is smaller when the brick is sunk. As less water is displaced, the water level in the pool will fall.
Just thought that was an interesting little tidbit. Until next time, here’s wishing you fair winds and following seas.
Brent Pounds has over a decade of experience in the maritime industry and has been involved in recreations boating since he was a child. See the About section for more detailed information.