 # What should be the speed of the urine stream for a man to fall from recoil if the penis is located strictly parallel to the ground?

## Beyond the Boundaries | Critical Role | Campaign 2, Episode 32

August, 2021

Let's say that the height, weight, foot size and diameter of the urine stream in a man is 1.74m, m = 68kg, l = 26cm and d = 2.5mm, respectively. The density of urine is approximately p = 1030 kg / m3. Let the penis be just below the middle of the height H = 0.45 * 1.74 = 0.783 m. Since a person tries to keep himself in balance, most likely the center of mass is in the middle of the foot. Based on these data, we write the equation of the moment, from where we find the pressure force of the urine stream. F * H> = l * m * g / 2, whence F> = l * m * g / 2 * H, whence F = 112.8 n. Now let's calculate the cross-section of the urine stream S = n * (d / 2) ^ 2 = 5 * 10 ^ -6. The dynamic pressure of the jet is pv ^ 2/2, where v is the jet velocity. So, pressure is by definition F / S. Let's equalize: F / S = pv ^ 2/2; v = sqrt (2 * F / p * S), whence v = 210 m / s, i.e. 754 km / h. So, for an average man, the required minimum jet speed for such purposes is 754 km / h (slightly more than half the speed of sound).

Who cares, here is the formula for an approximate calculation of the speed: v = 5 * sqrt (m * L / p * H * d * d), where d is the diameter of the jet, L is the length of the foot, m is the weight of a person, H is the height of a person, p is the density of urine. Count, tell, how many)

August, 2021

I won't answer your question, of course. But. To move a person from the spot, the jet must meet sufficient air resistance, which will still cause opposition. Let us assume that the head of the outgoing liquid is sufficient to form a clear rod (cylinder) from the jet. Taking into account that the radius of the cross-section of this rod is rather small, and in order to meet sufficient resistance, it is necessary to increase the head still (at that, multiple). Do not forget that a person is not a hose lying freely on the ground - a person's body stands on a support and is in a sense secured. We're dealing with a kind of tight fit. Legs will act as a shoulder of strength; I don’t think we will be able to win on this (record: Russian woman Nina Pylskoy has 123cm legs). It will rather be another challenge. It is also necessary to take into account the weather conditions (they should be taken as "normal", of course), take into account the density of the jet and its spraying.

I am studying to be an electrician-communicator, therefore the field of knowledge is not much further than electricity and telecommunications. I hope that the conditions described by me will help a person who knows hydraulics in conjunction with physics and applied mechanics to give an answer.

August, 2021

I think that at least km / h. Because this is the average speed of a pedestrian. If a person is standing, then recoil occurs at this rate and the person can be unbalanced, thereby he will fall.

Answer: not less than 2 m / s