Not homework, just a weird random question from my nephew.
Would rain drops be dangerous if there were no air?
That is, imagine here on Earth, it’s raining. Suddenly, all the air disappears, so now the rain drops can fall without air friction. Would the drops be painful? Dangerous?
I guess the answer is that the rain would just boil away because of a lack of atmospheric pressure. So, further imagine a liquid that is the same as water, but with a boiling point that was much, much higher, so that it remains liquid in a vacuum. Or, imagine a downward wind that moved exactly the same speed as the air at all times, so that there would be no terminal velocity.
I guess the fundamental question is, would rain falling from a cloud with no terminal velocity be dangerous?
Doing some rough Googling, the terminal velocity of a rain drop is 20 m/s and they fall from 2000 m. With no wind resistance, they’d hit at a speed of 200 m/s.
I would guess the height from which they begin to fall varies quite a bit, depending on the cloud involved. But if we stick with your impact velocity of 200 m/s, we end up with an impact pressure of 197 atmospheres. For us Americans, that’s 2900 psi. Pressures that high are commonly associated with hydraulic injection injuries. When these happen in industrial settings, it’s usually a small quantity, but the fluid involved is typically hydraulic oil, which produces toxic effects. Being caught out in a storm of high-velocity raindrops wouldn’t be quite as toxic, but the number of drops might get to be problematic; your scalp, shoulders and any other surface you presented to the sky would be peppered with little water injection sites. People would quickly learn to take severe storm warnings much more seriously, and umbrellas would be made out of much tougher material.
One other consideration is that wind resistance also limits the drop size but breaking apart larger drops. The possibility of larger drops through the accumulation of smaller drops is possible. However, given that there is no air to hold the drops up in the clouds to begin with, the rain would start falling at smaller drop sizes and rapidly all reach the same velocity in their vicinity. As such accumulation of smaller drops into huge drops isn’t really very possible.
Being hit by mist at 200 m/s would be no picnic either.
But really Disheaval’s point illustrates how an atmosphere-less planet couldn’t have anything like what we call rain on Earth.
Maybe we’d have to imagine a cryovolcano like we see on some moons out there in the solar system. They could throw out droplets of liquid substances that could then fall without much atmosphere to slow them down.
200 m/s is consistent with musket muzzle velocity. Diameter of a raindrop would be smaller and that means less mass. I don’t think one would kill you, but several thousand might.
On the upside, if we lost our atmosphere, I don’t think we’d have to worry about the hard rain. Rain comes from water vapor precipitating out of air as it rises and it’s pressure drops.
Rain falls from a lot higher than 2000m. Thunderstorms carry rain as hail up to darn near 10000m before it reverses direction and starts falling.
If we assume a raindrop is falling from 10000m in the absence of an atmosphere, it’d be doing ~442m/s at impact. That’s ~1450 ft./sec. Which is pistol bullet speed.
And absent air drag, there’d be no reason the drops couldn’t coalesce and get to be baseball-sized or larger. Which would be fatal if you took a single hit.
