Asklemmy

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

This sounds like the perfect thing for whatif by xkcd

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

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.

Your urethra is going to be really fucking sore.

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

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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.