Your penis is not a load-bearing structure. It's a hose.
You can't launch yourself from the power of your piss.
To start with, this is a conservation of momentum problem. Urine exiting into the atmosphere is at atmospheric pressure; you're not really pushing so much on the stream so much as you're experiencing the recoil from emitting it. Assume your urethra has an area of 10-5 m2 and your weight is 850 N (I think easier in SI, so I converted).
The impulse you need to provide = mass flow rate x average velocity. And mass flow rate = volume flow rate x density. Volume flow rate = average velocity x cross sectional area. So we have an equation: 850 N = ρAV2. Assume here that urine and water have the same properties, so density = 999 kg/m3. We therefore get average velocity = 292 m/s, which is about the speed of a commercial airliner.
So now we know the velocity we need, but how much pressure do you need to exert to achieve this velocity?
That's a flow problem. We get the diameter of the urethra from the cross-sectional area, about 0.0036 m. Now we have enough to calculate the Reynolds number, ρVD/μ. This is about 9.3 x 105, so we have turbulent flow. Assuming a roughness of 0.045 mm (typical for a decent quality pipe, and probably similar for a human body), we have a friction factor of 0.043. We also assume that the urethra is 0.20 m long and the vertical drop is negligible compared to the pressure we'd need. A modified form of the Darcy-Weisbach equation, ∆p = γf x (l / D) (V2 / 2g) gives us a pressure drop of 102 MPa, or about 15000 psi.
Good luck with that.
TL;DR: 15,000 psi
The PSI of a erection:
1400 mmHg = 27 PSI
From Beckett, "Blood Pressures and Penile muscle activity in the stallion during coitus" Am J Phys, vol. 225, no 5, 1973
For stallions: 6530 mm hg = 126.3 PSI
For goats: 7003 mm hg = 135.4 PSI
For bulls: 1727 mm hg = 33.4 PSI
In metric boner pressure:
Humans - 1,7 bar
Stallions - 8,7 bar
Goats - 9,3 bar
Bulls - 2,3 bar
TL:DR > Even if you sustained a erection while pissing hard enough to fly, your dick would still fall apart.
Name:
Anonymous2012-09-27 11:52
Exploding "peen" from jizzing too hard? That's a terrifying concept.
Name:
The Math2013-04-09 21:16
THE MATH
Psychologist : "WHY IS IT "CAN I GIVE YOU MY TWO CENTS," BUT THEN IT'S "A PENNY FOR YOUR THOUGHTS"?"
Patient : "BECAUSE IT SHOULD COST TWICE AS MUCH TO TALK AS IT DOES TO LISTEN."