How much WR is needed for rain? A few calculations....

# Thread: How much WR is needed for rain? A few calculations....

1. ## How much WR is needed for rain? A few calculations....

I thought I'd do these calculations, seeing that my Physics exam just got over.

From Wikipedia, I found that the maximum radius of a pure rainwater drop is 5mm(5x10^-3m)
and its terminal velocity while falling in air is 16.5m/s.

So, mass of the droplet= Volume x Density
=4/3 x pi x r cubed x 1000kg/m^3
=0.000523kg.

The momentum of the droplet= Mass x Velocity = 0.000523 x 16.5 = 0.00863 kg m/s

The area this force will be spread over = area of the circle with radius of the droplet
= pi x r^2
=0.0000785 meter squared

So, the force applied = dp/dt (rate of change in momentum)
(I'm taking that the velocity of the water becomes 0 after impact)

I'm not too sure about the time it takes for a droplet to stop, but I took it as 0.5 s.

F= 0.00863/.5 =0.01726N

Pressure = Force/Area = 0.01726/0.0000785 = 220 Pascals.

This is equivalent to the force exerted by 'y' m of water.
220=y x density x acc. due to gravity

y= 0.02m = 2cm
After adding atm. pressure, the WR needed to be rain proof is 10.02m.

I think this value is too low. Probably the time it takes for the drop to stop moving is less than 0.5 s.

Does anyone have any idea what the value for time is?

PS: When I take time as 0.1s, then the pressure comes out to be 11cm of water. Which would mean a WR of 10.11m is needed.

So does this mean that 30m WR resistance is enough for rain?

2. ## Re: How much WR is needed for rain? A few calculations....

While I think 30m WR is more than enough for rain, I think your calculations may have been a bit hinky..... Im pretty sure you calculated the area of the circle as having radius 5, but that will give you an artificially low value. The correct radius should be a lot larger (not sure exactly how high, but remember that the sphere flattens out upon impact, putting all of the volume into one very thin and wide cylinder).

I like seeing physics and other science on here though!!!! And welcome to the forums.

3. ## Re: How much WR is needed for rain? A few calculations....

I would say 30M WR is enough for rain. I am also a physicist and rather enjoyed the way you thought the whole thing through. Remember, the water resistance is only what is applied at the seals - its not like raindrops are hitting directly on the seals - they tend to fall on the case or the crystal, and then trickle to the rubber seal, at which point the "pressure" of a falling raindrop becomes rather negligible (but, as any good physicist would say, not insignificant!). Now if you were underwater, the depth you happen to be at will exert a constant pressure on the seals assuming a stationary watch. Thats where the depth and pressure ratings become more relevant.

4.

5. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by Eric L.
I would say 30M WR is enough for rain. I am also a physicist and rather enjoyed the way you thought the whole thing through. Remember, the water resistance is only what is applied at the seals - its not like raindrops are hitting directly on the seals - they tend to fall on the case or the crystal, and then trickle to the rubber seal, at which point the "pressure" of a falling raindrop becomes rather negligible (but, as any good physicist would say, not insignificant!). Now if you were underwater, the depth you happen to be at will exert a constant pressure on the seals assuming a stationary watch. Thats where the depth and pressure ratings become more relevant.
but Eric--keeping in mind I'm physics-lite--there are raindrops that will be hitting directly on the seals, maybe not every time, but sometimes. Like the lottery. And do we want watches to protect us from such rare occurences? Apparently yes.

6. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by Sean779
but Eric--keeping in mind I'm physics-lite--there are raindrops that will be hitting directly on the seals, maybe not every time, but sometimes. Like the lottery. And do we want watches to protect us from such rare occurences? Apparently yes.
The seals on a watch aren't exposed enough for a raindrop to hit it dead on - it would likely dissipate on both the seal and the surrounding caseback or crown. Same for the seal around a crystal.

7. ## Re: How much WR is needed for rain? A few calculations....

and really, the dive watch industry is built on impossible eventualities that we whittle down to: we hope our 10,000ft diver is at least 200m waterproof, deep as most divers go. We want 10,000 ft. depth ratings because we have little confidence in depth ratings because our dive watches are not tested individually. This is crazy (and reality) to me--that commercialization/capitalism produces a product for profit gain rather than excellence. Fine, the necessary demands of overpopulation and billions of consumers. We're not getting, as divers, an adequate product, too small a market.

8. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by Eric L.
The seals on a watch aren't exposed enough for a raindrop to hit it dead on - it would likely dissipate on both the seal and the surrounding caseback or crown. Same for the seal around a crystal.
ok

9. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by Sean779
and really, the dive watch industry is built on impossible eventualities that we whittle down to: we hope our 10,000ft diver is at least 200m waterproof, deep as most divers go. We want 10,000 ft. depth ratings because we have little confidence in depth ratings because our dive watches are not tested individually. This is crazy (and reality) to me--that commercialization/capitalism produces a product for profit gain rather than excellence. Fine, the necessary demands of overpopulation and billions of consumers. We're not getting, as divers, an adequate product, too small a market.
Sure, impressive sounding numbers sell. But what does that have to do with using some physics and math for a thought experiment? OP asked what WR was necessary to withstand a raindrop, not why people want 1000M divers.

I have divers from every single depth rating (ok maybe except for 10,000 feet) and to be honest the depth rating doesn't matter as much as the styling and the feel of the watch. I'm not even sure I believe some of the divers with big numbers would survive at their rated depth, but I'll never find out since the wettest mine get are a few feet underwater.

10. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by mike120
The correct radius should be a lot larger (not sure exactly how high, but remember that the sphere flattens out upon impact, putting all of the volume into one very thin and wide cylinder).
Heh, I left out a few of the assumptions I made... I was trying to get the maximum value of pressure that could be exerted on the watch, so you could have a 'max' value to base WR on.

Thanks to everyone for reading and commenting!

11. ## Re: How much WR is needed for rain? A few calculations....

Originally Posted by TheWanderer
Heh, I left out a few of the assumptions I made... I was trying to get the maximum value of pressure that could be exerted on the watch, so you could have a 'max' value to base WR on.

Thanks to everyone for reading and commenting!
Makes sense to me!

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