Can three inches of rain kill you?

[Sakiale]

Not lethal, not lethal. But yeah, I was thinking it might cause you to stagger a bit.

 

[Philly]

He's in a physics class. He could run a few experiments to see just how water breaks up and measure what force is "dissipated" with breakup. BL's figure is worst case scenario, where the water hits your head and stops.. In reality, most would be deflected a little.

 

[Sharky.]

Terminal velocity = (2W/CDAp)^0.5

Sure, I take Physics at school, but we don't use formulas like that

Maybe when I hit university next year...

W = 5.3 * 9.81 = 51.993 N
For a square prism with b = h, CD = 1 for Reynold's number > 1000. 26 x 27 cm is close enough....
A = 0.0702 m^2
p = 1.2 kg/m^3 for atmospheric air

You, sir, make my head hurt

 

[Danoff]

Terminal velocity = (2W/CDAp)^0.5

Just going back to ExigeExcel's example where he provided a few measurements:

W = 5.3 * 9.81 = 51.993 N
For a square prism with b = h, CD = 1 for Reynold's number > 1000. 26 x 27 cm is close enough....
A = 0.0702 m^2
p = 1.2 kg/m^3 for atmospheric air

So, this hypothetical sheet of water will hit you with a velocity of 35.134 m/s provided it's falling from a high enough altitude to attain terminal velocity (which it undoubtedly is).

The kinetic energy of the body of falling water is then 3271.15 J


...I think it could hurt, but I don't think it's lethal force though. Unless you're wearing a basin on your head you aren't going to recieve the water's full energy as blunt trauma. But I don't know enough about how water behaves under direct central impact to make any sort of guess at how much energy you do take from the collision.


It'll muss up your hair.

This is good analysis, but it depends highly upon the surface area - meaning that we need a good definition of the size of the magical block of water that stays glued to itself until impact.

For example, if 3 inches of rain water were magically glued to itself until it hit the ground, and it covered the entire earth... it would not hit the ground. The air beneith it would compress until it could compress no more, at which point the water would be suspended in the air. Make the block the size of a continent and it would fall quite slowly as the air would have to rush out from undernieth it very fast (it might get windy under there). Make the water too small and it doesn't have enough weight to impart much force.

There is an optimization problem here, surface area vs. weight, at which we can find the maximum impulse delivered by the water block.

Basically though, drag is going to prevent this from getting interesting. If a person jumps from very high into a body of water, that person's terminal velocity is high, and so it can be deadly. If a body of water jumps onto a person, that water's terminal velocity is going to be low and so it isn't going to do much damage.

As a side note, water can be thrown at you fast enough to kill you. Some water is used for cutting materials, and so it could probably be used to cut you in vital places as well. But this water isn't just falling, it's shot out very fast and in a focused stream. That's much different than water naturally falling through the air.

 

[Sakiale]

If a body of water jumps onto a person

 

[Boundary Layer]

This is good analysis, but it depends highly upon the surface area - meaning that we need a good definition of the size of the magical block of water that stays glued to itself until impact.

...

There is an optimization problem here, surface area vs. weight, at which we can find the maximum impulse delivered by the water block.

...it doesn't depend on surface area as much as you think.

The lowest CD you'll get for a rectangular prism moving through a fluid is 1.05 (when b = h). Since we're keeping the thickness of the sheet constant at 3" the weight basically becomes a function of surface area, or b^2 as the case will be.

So, for a water density of 998 kg/m3, t = 3" = 7.62cm, and g = 9.81m/s^2:
m = t(b^2) x 998
W = mg

Then, in the formula: Terminal velocity = (2W/CDAp)^0.5
the b^2's will cancel, leaving

Terminal velocity = (2(0.0762)(9.81)(998)/(1.05)(1.2))^0.5
Terminal velocity = 34.412 m/s

(note, this is less than the previous velocity because I used rounded values in the previous calculation)

That is, for a fixed thickness, and constant air and water density, the only optimization you have to make is to take a square profile, the physical dimensions of the square sheet do not seem to affect the terminal velocity, but will affect how quickly the body of water will accelerate due to gravity against the drag.

What you're suggesting Dan is more of a fall height vs A optimization.... take the highest possible fall height and adjust A so that terminal velocity is attained just prior to impact.
I suppose in your suggestion you would have to look at the effects of the compressibility of air under the sheet but that is well beyond the scope of this thread. I haven't done the math there, but I think the sheet would be so large before this became a factor that the majority of the sheet would miss the targetted human anyways. I'm assuming the sheet is small enough that the compressibility of air is negligible.

As a side note, water can be thrown at you fast enough to kill you. Some water is used for cutting materials, and so it could probably be used to cut you in vital places as well. But this water isn't just falling, it's shot out very fast and in a focused stream. That's much different than water naturally falling through the air.

ahh, water jets are cool 👍

 

[dylansan]

Wouldn't it be just like falling through a sheet of 3 inhes of water, headfirst? Dump an ocean of water on you, and you are'nt going to survive. Dump 3 inches, and you'll be fine. I'm not a physicist, but I don't hink it would be painful, at least not just from the impact of the water.

 

[Gil]

Did you need a shower anyway?

If the field is of sufficient size, you could concievably get squished.

I'm pretty sure if you fell from normal cloud height into a three inch puddle you would surely die.

If that three inches of rain is on the ground in a three inch deep puddle, and you just happen to be ass-up with your face buried in that puddle, you will die in about 4 minutes.

If it falls on your head, it would disperse. This would leave you quite wet. If the temperature was low enough, and you stayed out in it long enough, you could die of hypothermia.

 

[Philly]

If it falls on your head, it would disperse. This would leave you quite wet. If the temperature was low enough, and you stayed out in it long enough, you could die of hypothermia.

So, to answer the question, yes. 3 inches of rain can kill you.

 

[Dave A]

The bottom line is, a 3 inch thick blanket of rain falling should not kill you upon impact. The dying of hypothermia is a sepetate argument dependant on more factors than the original question in this thread, but yes it an cause hypothermia and the hypothermia can kill you.

 

[Danoff]

That is, for a fixed thickness, and constant air and water density, the only optimization you have to make is to take a square profile, the physical dimensions of the square sheet do not seem to affect the terminal velocity, but will affect how quickly the body of water will accelerate due to gravity against the drag.

At some point your CD assumption breaks down. CD depends on area, which is why terminal velocity is not solely determined by thickness in all cases.

What you're suggesting Dan is more of a fall height vs A optimization.... take the highest possible fall height and adjust A so that terminal velocity is attained just prior to impact.

Why would the time at which the sheet attained terminal velocity matter? As long as it was going top speed, it imparts the most energy. But you effectively answer my question below.

I suppose in your suggestion you would have to look at the effects of the compressibility of air under the sheet but that is well beyond the scope of this thread. I haven't done the math there, but I think the sheet would be so large before this became a factor that the majority of the sheet would miss the targetted human anyways. I'm assuming the sheet is small enough that the compressibility of air is negligible.

You're right about the surface area of the target being fixed. The maximum impulse fom the water is determined by the amount of water that hits the person, not the total amount of water. Water that doesn't hit him is useless.

So we should assume that the water sheet has roughly the same surface area as the top of a person's head, and hits him on the top of the head. Any more water than that is useless because it either doesn't hit him, or doesn't hit him in a way that would be lethal.

Your 34.4m/s converts to 76.95 mph. I doubt that would be lethal.

 

[Boundary Layer]

At some point your CD assumption breaks down. CD depends on area, which is why terminal velocity is not solely determined by thickness in all cases.

Fair enough, I'll take your word on it. My fluids prof always stated that the CD was only dependent on the aspect ratio of the planform area for rectangular plates normal to flow, and not on the area itself - but it would not be the first time he was wrong.

Why would the time at which the sheet attained terminal velocity matter? As long as it was going top speed, it imparts the most energy. But you effectively answer my question below.

You're right about the surface area of the target being fixed. The maximum impulse from the water is determined by the amount of water that hits the person, not the total amount of water. Water that doesn't hit him is useless.

Yeh, I misinterpreted your earlier statement since your post up to that point had been mostly about really big sheets. I think the maximum deliverable impulse of the sheet of water would involve optimizing area and fall height, assuming the target is large enough to be struck by the entire sheet - and this is the situation I thought you were talking about.

I agree with your statement in the case that you're only interested in finding the largest possible impulse in the collision between the water and the human.

 

[UnoMOTO]

We see people survive this all the time. Even with the increased velocity of water of the bucket it doesn’t do anybody any harm.

 

[Perfect Balance]

I had a (about) 1 foot diameter water balloon thrown at me from a balcony around 15ft up. More water + gravity and the force from the throw. It just felt like a lot of pressure all at once, but not painful at all.