Question: What happens to your weight when you fart?
Short answer: It increases.
Long answer: Farts are mostly made of carbon dioxide and hydrogen. The exact composition varies from person to person, but hydrogen is likely more prevalent, with some studies finding a ratio of about 5:1 by volume (Tomlin, Lowis, and Read, Gut, 1991).
If farts are mostly hydrogen, then they have the property of buoyancy, first discovered by Archimedes of Syracuse in 212 BC.
Buoyancy is an upward force that resists gravity, for an object that is less dense than the surrounding medium. The fact that hydrogen has a lower density than dry air gives it excellent lifting power, so that it can be used effectively in hot air balloons. The flammability of hydrogen does raise certain safety concerns in this regard.
The lifting force exerted by hydrogen is given by the buoyancy equation:
where g is the force of gravity, V is the volume of gas, and ρ is the density of air or hydrogen. It is well-established that g = 9.8 m/s2; the volume of hydrogen in a fart is 100 mL; the density of air is 1.292 kg/m3; and the density of hydrogen is 0.09 kg/m3. We therefore arrive at the buoyancy of a fart:
Hydrogen trapped in the rectum therefore exerts an upward force of 0.0012 N, which opposes the downward force of gravity, which is 9.8N. As a result, if one farted while standing on a scale, the change in weight due to hydrogen release would be an increase of 0.01%.
For most humans, this is a negligible amount of weight, but for other animals, it can be quite substantial. Indeed, experimental observation has determined that manatees fart when they want to sink deeper into the water, as documented here: