How much flow and volume from urination do you need to levitate your whole body for two seconds off the floor?
How much flow and volume from urination do you need to levitate your whole body for two seconds off the floor?
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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.
For reference, 3 km/s is approximately Mach 10
Fuck yeah science
What a fun way to find out my bladder capacity is around three times the average at least. Connective tissue disorders are whack. Now I've just gotta work on the other factors so I can piss-levitate longer than everyone else! I'll be unstoppable!!