The Pee Velocity - Male Version

the other day i took a piss in the shower (actually, i left a piss in the shower rather than taking one) and i wondered about the velocity of the urine which left the "old chap".

if, for example, the pee began at a height of 1 meter and landed at a distance of 1 meter and took, let's say 0.2 seconds to hit the drain, then the velocity can be found in this way:

x-velocity = 5 m/s

if it went 1 meter in 0.2 seconds, then it will go 5 meters in 1 second. so the x-velocity is 5 m/s.

y-velocity = 4.02 m/s

if the urine began at a height of 1 meter and 0.2 seconds later it hit the drain, we can find the y-velocity with the following equation:

P (for position...not pee) = Voyt - 1/2gt^2 (t = time and g = gravity at 9.8 m/s...if i were pissing on the moon it would be a different story, all together...well come on! let's say it all together!)

plugging in the numbers we find:

-1 = Voy*0.2 - 0.196

after rearranging the equation to solve for Voy, we find the y-velocity is 4.02 m/s

v = 6.416 m/s

the velocity of the pee exiting das wienerschnitzel is the square root of x-velocity squared + y-velocity squared.

6.416 m/s. that's about 23 km/h. it would be like running the 100 m at the olympics in a time of 15.59 seconds. it's not a gold medal time....but it may be a golden shower medal time.

well, let's find the angle now shall we?

angle = 38.799 degrees below level

the angle of the dangle can be found by taking the -cos of dividing the x-velocity by the velocity, or by taking the -sin of dividing the y-velocity by the velocity.

or you can always just do the old arctan of rise over run. in other words the arctan of y-velocity/x-velocity.

so next time you're taking a whiz in the shower, i hope you appreciate the physics involved in such a simple every day act.

p.s.
these calculations are also valid if you're pissing in the toilet.

addendum

the length of the piss stream can be approximated by dividing the time it takes to land into small segments, say for example 40, and then dividing the x-distance by the same amount. so we would have time segments of 0.004 seconds and x-distance segments of 0.02 m.

for each of the forty 0.02 x-segments we can calculate the distance that y would be after 0.004 seconds then add up all the little hypotenuses (or hypoteni if you prefer).

i took the liberty of baking one earlier and when i pull it out of the oven, we have an approximate stream length of 1.417 m.

now...on to a new pondering.

suppose we turned that 6.416 m/s velocity piss stream skyward. what's the maximum height we could achieve?

the maximum height would be if we aimed our urine straight toward heaven at a 90 degree angel...i mean angle. we could reach the dizzying height of 2.1 m. that's 2.1 m away from the willy and 3.1 m above the ground. holy doodlebugs!

at a 45 degree angle we could achieve maximum distance. here we would reach a height of 1.05 m, with a range of fully 5.034 m when it hits the ground. and a piss arc (not to be confused with the BC border crossing, the peace arch) of approx. 6.133 m that's a 4.82 m arc from a starting position of 1 m, up to a 1.05 m max. height, then back down to 1 m [where at this point it is 4.2 m away]. then from there, the stream will add another 1.313 m to its arc length until it finally and mercifully strikes the ground 5.034 m away).

just thought i'd share that with you.

tomorrow we'll discuss the tao of poo.