# Float vs Sink - Salt Water vs Normal Water

My buddy was telling me a story about a long sailing trip he took where he had to drop a number 2 when swimming. He told me his biggest concern was worrying if it would float and touch him. Lucky it was a sinker.

This lead to a series of questions and discussion between us, that boiled down to if dropping a number 2 in salt water has a higher chance of a floater than a number 2 in non salt water. Hoping someone has insight.

Your poo does experience more buoyant force in sea/salt water compared to fresh water because the density of salt water is higher than that of fresh water (assuming fresh water is synonymous with pure water). Whether or not your poo floats or sinks, however, largely depends on the composition of your poo (what you ate, amount of compression, water content, fibre content, etc.), not the concentration of salt in the water.

We can start from the assumption that most poos are of similar total volume. By Archimedes' Principle, the upward buoyant force that the poo experiences in a fluid is equal to the weight of the fluid displaced. Salt water and pure water do not differ significantly when it comes to densities (~$1000kg/m^3$ vs ~$1025kg/m^3$). Estimating your poo to be

$10cm\times10cm\times10cm=1.0\times10^{-3}m^3$

(which is a decent size for a poo), the difference in buoyant force will ever only be at most $0.25$ Newtons or so compared to the weight of an average poo of ~$1.3$ Newtons. Note that what I have done here is estimate a big volume of stool, calculate the difference in buoyant forces experienced by that volume of stool in salt vs pure water and then compare that to the weight of an average stool. This means that for any volume less than that (assuming similar stool mass), the buoyant force is even less significant. Implicit is the assumption that stool does not get significantly larger than that volume without a corresponding increase in mass.

Although there might be a type of stool where the difference in densities between salt water and pure water would matter enough for the stool to float in pure water but sink in salt water, I think that this scenario is unlikely (the stool would have to have a combination of large volume and low mass that doesn't quite qualify it as stool, much closer to diarrhoea). How salty the water is doesn't count as much as the type of poo you're pooing.

• How do you get from volume to buoyancy without knowing mass or density? – sammy gerbil Apr 16 '17 at 1:51
• The volume of the fluid displaced is all I need to know since I have the density of the fluid displaced, I can then calculate the mass of the fluid displaced. And then the weight. – HsMjstyMstdn Apr 16 '17 at 2:15
• You are comparing the buoyancy force on an estimated stool volume with an unrelated figure for the mass of a bowel movement. You seem to have a stool density of about 1.3/0.25 = approx 5x the density of water, which does not seem reasonable considering that there is a fine line between floating and sinking. – sammy gerbil Apr 16 '17 at 2:27
• I understand the importance of distinction of the stool's density here but what I meant to show was that for the approximate max (upper estimate) volume of a stool, the difference in buoyant force is small compared to the average mass of a "one" stool. I make no claim of the volume of the stool being connected to its mass, as this varies greatly among stool types. I merely "guessed high" on the volume, calculated the difference in buoyant force based off of that and then compared that to an average stool's mass. I will include this to clarify my answer. – HsMjstyMstdn Apr 16 '17 at 2:52
• OK sorry I misunderstood. You are comparing the difference in buoyancy between salt water and pure water. – sammy gerbil Apr 16 '17 at 3:19