How much flow and volume from urination do you need to levitate your whole body for two seconds off the floor?

This sounds like the perfect thing for whatif by xkcd

According to one of my favorite shorts of all time, the answer is “I don’t know”

Aerospace engineer here. To levitate, the force of the exhausted mass flow (F=ṁ×v) has to equal the pull of gravity (F=m×g) on your body. The gravity of earth is g=9.81N/kg. Wikipedia says the average body mass is 62kg. It also says the bladder capacity of an adult is about 400ml, and I'll assume the density to be 1kg/l. You want to levitate for 2 seconds, so your mass flow needs to be ṁ=0.4kg/2s=0.2kg/s. If you rearrange the equation, you get v=m×g/ṁ=62kg×9.81N/kg/(0.2kg/s)=3041m/s.

So if you manage to pee with a velocity of about 3km/s, you can levitate for 2 seconds with an average sized bladder.

To achive that, your "exhaust" must be clenched to a diameter of about 0.29mm. This gives a cross-section of 0.066mm² or 6.6×10^-8m². Multiply that with the velocity of 3041m/s and you again get your flow of 0.2l/s.

Of course, during those 2 seconds you loose mass and therefore, earth's pull on you gets less and you start to accelerate to about 0.23km/h, reaching a height of 4cm. If you took your special bladder to space, we can use the rocket equation to calculate that this stunt would accelerate you to 3041m/s×ln(62kg/61.6kg)=19.7m/s=71km/h

Beautiful, I was waiting for an engineer to do the calculations .... so in layman's terms, clench your urethra, push your bladder as hard as unhumanly as possible and hope to everything that is holy that your entire urinary tract doesn't explode before your urine leaves your body.
- It's not a question of if your urinary tract will explode, but where.
- For reference, 3 km/s is approximately Mach 10
Fuck yeah science
Will the density of my pee affect this?
- frantically starts drinking heavy water
- Yes, higher density means you exhaust more mass during those 2s, and therefore you don't have to pee so fast.

For a water powered jetpack to lift a person it is estimated to need at least 100 gallons per minute, so similarly this could be what would be needed. Even for a second, a person's bladder would need to be 1.6 gallons and expelled at a similar pressure. So not two seconds.

3.2 gallon bladder to achieve 2 seconds? And what kind of pressure are we talking, would it just like totally blow your dick off or what
- I mean a bladder can't even hold a fifth of a gallon (more like 500ml) so we are already saying it is not possible but assuming there in the future is a human cyborg or a robot the same mass and volume as a human, they would need 60psi and 3.33 gal capacity for two seconds. This info is based on water powered jetpack companies that do this service. So, I did over look one thing: the jetpacks are dual and attached to your legs and they happen over water so not sure the rest of the calculations because I am not certain whether each jetpack has same psi for it to work or it is a combined psi and the water just comes from a hose so there is no capacity but the speed needs to be at least 100gpm.
- Well, for a minute of water jetpack it is 100 gpm, so I divided 100 by 60 seconds to get 1.6... for one second so two it would be 3 and a third gallons for two seconds assuming the right pressure of 60 psi.
- pretty sure it'd blow more than just your dick off. it'd be a pretty gruesome scene.

Your urethra is going to be really fucking sore.

Flipped inside out, even.

I implemented a realistic physics simulation that answers this question for Diarrhea.

wow I just checked out the source, and as a physicist I can verify that some of those fluid dynamic models you implemented are very cutting edge
"realistic" lol
Beautiful .... bookmarked and saved ... my personal best so far is 1023 m

Enough that your abdomen would likely explode from the pressure. Which would make some percentage of your body fly, technically.

Comments are locked. This question has been answered.

Force = Mass * Acceleration.

Gravity is (approximately) 9.88 m/s^2.

According to a random Wikipedia page, ideal body weight was at one point considered 50kg.

This means that the following will find the point where you are perfectly neutral, neither rising off the ground nor being held down by gravity:

9.88 * 50 = M * A

Unfortunately, A in your scenario is 0, meaning that this is not possible no matter how much piss you have. This is because your urine basically just falls out of your body and isn't being ejected with force.

I question your statement of , it just falls out. If it only fell out you couldn’t piss any distance other then down. Yet you can get quite the distance. So there has to be some force there. Although it would be quite small
- So technically, you are correct. The force is the water pressure provided by the piss being pulled down by gravity. Practically speaking, this force is negligible because all you're doing is allowing the piss to fall, not forcing it downwards.
  
  Basically, imagine you're holding an incredibly heavy rock that does not have a gravitational field or air resistance. If you drop the rock, gravity will pull it down, but regardless you will not go up unless you apply force and throw it down.