Assuming a full bladder, and a constant direction. In physics I know that Force=Mass (Times) Acceleration, but I know neither Mass nor Acceleration, so I cann’t find the force.
Also, if you were in space (ie on a space station with lots of room to move around) could you blow your self around, as in the Rolald Dohl book were the people go into space in a glass elevator, and need to blow air out of their mouths to move around?
Thanks in Advance!
For Mass, urine can be assumed to be roughly equivalent to water, thus “a pint’s a pound” would apply. And average bladder capacity is about 1 to 1.25 pints (16-20 ounces) (though this seems to vary by age, gender, racial background, and the individual). So you can make a reasonable estimate for Mass.
Acceleration would vary, since it is controlled by muscles, not gravity. (Proven by Nobel Laurate Dr. Feynmann years ago in an experiment at Cornell(?) University, mentioned in one of his books. Easily duplicated: stand on your head in the shower, and see if you can still pee.) I’d think it would depend on the strength of those muscles in each individual. Also, this is somewhat under voluntary control – I know I can use more ‘force’ if I try.
Some time ago, an IBM publication had an article on ‘human-powered computers’.
It discussed making a small, wearable computer that needed no outside power source, but used human body functions to generate it’s operating power. The main ones they discussed were using body heat to generate power, minature generators powered by the movement of your arms & legs, and pressure generators located in your shoes. Their assesment was that this was possible, given a very energy conserving CPU, etc. (This was at least 10 years ago; would probably be even more feasable today.)
But this article neglected any use of a couple of power-generating bodily functions, probably out of a corporate concern for propriety. No consideration of the possible power to be generated from human farts, or the OP’s topic, the thrust of human urination.
I know a way to calculate it, but it’s icky on the Mythbusters level of ickyness.
Get a graduated/measured container and “make use” of it at a measured distance–horizontal to your “expulsion device”. Measure the time it takes to get to a specific volume. You may need to practice, and this presumes you’re male.
Now we have time to move a known volume and a ballistic trajectory. A little calculation could solve the puzzle. I’m not going to do it.
Another way would be to lie on one’s back and measure the height achieved. Like pumps are measured. The height (pump head) a pump will lift liquid.
Warning! Always engage excretion seal securely and fasten uniform tethers before urination. Failure to do so may result in unintended acceleration, and, um, you don’t want to know what else. :eek:
It would seem the best way to done this might be to calculate the volume of urine deposited within a specific time.
Based on this page about catheters most male urethral lopenings are 4-6 mm in diameter. If an energetically urinating man can move enough urine fill a 16 oz soda bottle in 10 seconds through a 5 mm urethral opening, how fast does the fluid stream have to be moving to accomplish this?
It should be easy to measure urine flow speed. Just see how far you can pee. The distance only depends on initial height and initial velocity, and the maximum distance only depends on initial height and initial speed.
So who has the data points?
Let us estimate the nozzle (heh) velocity v. Say it’s approx 0.75m above the water, and moves forward 0.5m in this fall. The equation of the arc would be y=0.75-Ax[sup]2[/sup], and solving for 0=0.75-A0.5[sup]2[/sup] gives A=0.75/0.25=3. But x=vt, so y=0.75-3v[sup]2[/sup]t[sup]2[/sup]. Differentiate: y’=-3v[sup]2[/sup].2t and again: y’’=-6v[sup]2[/sup]. But y’’ is -10 (acc’n due to gravity) so v is sqrt(1.67)~1.29m/s. That seems a lot, did I make a mistake?
Anyway, then assume 0.5kg of urine and a 100kg person - he’d be going backwards at about 0.006m/s?
Guys, you’re making it all too hard. Just ask the resident rocket scientist. 
(Okay, so my title is aerospace engineer, not rocket scientist…but who’s gonna argue?)
The equations for thrust is net momentum flux (mass flow rate times velocity) plus the force of the pressure differential (difference between exit and freestream pressurs times exit area)
Here, mass flow rate (m is the closest I could come to "m dot," which is dm/dt) is how much mass leaves the urethra every second. Normally, m= p · V · A, but in this case, it’s easier to calculate by dividing mass expelled by time it takes to do so. so m` = (total mass of urine)/(time of urination)
T = (m V)[sub]e[/sub] - (m V)[sub]0[/sub] + (p[sub]e[/sub] - p[sub]0[/sub]) · A[sub]e[/sub]
Now, the freestream momentum is effectively zero, since the fluid velocity in the bladder is negligible. The pressure difference across the urethral opening is very small, and acts over a miniscule area, so the last term can also be ignored. This reduces our thrust equation to:
T = m` V
(simple, huh?)
Using the numbers from astro’s page about urination, we can calculate mass flow rate and velocity. m = 1 lb[sub]m[/sub] / 10 sec = 0.00311 slug/s. And from my above equation, V = m/(p · A)
m` = (0.00311 slug/s)
p = water = 1.94 slug/ft[sup]3[/sup]
A = area of 5-mm diameter circle = pi · (0.0082021 ft)[sup]2[/sup] = 2.113×10[sup]-4[/sup] ft[sup]2[/sup]
V = (0.00311)/(1.94 · 2.113×10[sup]-4[/sup]) = 7.585 ft/s
so T = m`· V = (0.00311 slug/s)(7.585 ft/s) = 0.0236 lb (or 0.67 g)
It’s a rough order of magnitude apprximation to be sure…but there you go.
(About halfway throguh this calculation, I was reminded why I hate British units. Slugs…what? But the soda bottle numbers were given in oz, so I had to convert something. I obviously chose wrong. Kill me now. 
)
Man you guys pee a lot. Over a pound of urine?
Guess I need to drink more water!
Just realized a mistake… 0.0236 lb is 10.71 grams-force or 0.105 Newtons.
Sorry about that…got my unit conversions mixed up. I work for the government, what do you expect?
If you’ve had a lot to drink an average man can easily fill 2 16 oz soda bottles (or more).
A lot more if you’ve been drinking beer.
It is almost impossible to calculate the acceleration and it is unnecessary. There is a simpler way based on conservation of moment. If you eject m mass at v speed north then your body of mass M will move south at speed V= m*v/M
I have some experience peeing into cans (peeing over the rail often made a mess even to leeward what with wind shifts and gusts) and I was always surprised to see how consistent the volume was and which I calculated at about 350 cc (.77 lbs). I guess I have a small bladder compared to other guys around here.
Excuse me, #1 is calling. BRB.