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Treebeard's Stumper Answer
3 March 2000

The Sky is Falling

We've had rain, rain, and more rain lately here in central California! Think of the weight of all that rain up in the clouds before it falls. A gallon of water weighs about 8.3 pounds. A cubic foot is about 7.5 gallons, so a cubic foot of water weighs about 8.3 x 7.5 = 62 pounds. And so a storm cloud that drops one inch of rain holds about 62 / 12 = 5+ pounds of water per square foot. A cloud one mile on a side is 5,280 x 5,280 square feet. That comes to 1.4 billion pounds of water per square mile of cloud! How can that much water be floating in the air above us? Why doesn't it all fall at once?


An inch of rain weighs 5+ pounds per square foot, but that water is spread out as tiny droplets in the cloud it falls from. If the cloud is 1000 feet thick, that water is dispersed over 1000 vertical cubic feet, only 0.08 grams per liter. The air holding those droplets weighs 1.2 grams per liter, many times more. Water droplets are subject to gravity, but they are so tiny that air currents have a greater effect in keeping them aloft, like dust motes. If they coalesce into larger drops, they fall as rain. And sometimes clouds do fall, and become... fog!

Notes:
Gauls! We have nothing to fear; except perhaps that the sky may fall on our heads tomorrow. But as we all know, tomorrow never comes!!

- Asterix The Gaul    

I should show my work for this answer, since I insist on it in school.

  5 pounds          pounds   454 grams    1 foot    1 foot    1 foot                               
  -------- = 0.005  ------ x --------- x ------- x ------- x -------
  1000 ft3           ft3      1 pound    12 inch   12 inch   12 inch

                    grams   1 inch    1 inch    1 inch    1000 cm3
           = 0.0013 ----- x ------- x ------- x ------- x --------
                    inch3   2.54 cm   2.54 cm   2.54 cm    1 liter

                    grams
           = 0.08   -----
                    liter
There's no need to stop there. Since a liter is 1000 cm3, and a cubic meter is (100 cm)3, we can also figure this as
                   grams   1 liter    (100 cm)3
           = 0.08  ----- x -------- x ---------
                   liter   1000 cm3    1 meter3

                   grams 
           =   80  ------ 
                   meter3
It's easier just to multiply by 16, but I always seem to get those special conversion factors wrong when it matters. With unit multipliers, I only have to remember a few numbers, and I always get it right. I wish I could remember which teacher to thank, though I probably thought differently at the time!

My number is actually about 10 times larger than other estimates I've seen for the water content of clouds. I was thinking of our typical California winter storm that comes in as relatively thin nimbostratus clouds. Thunderheads are much thicker. I think the real reason my estimate is too large is that our rain clouds are moving past us as the storm tracks from west to east. That inch of rain on the ground comes from a greater area of cloud in the sky.

On the other hand, these Pacific storms continue to track across the country, dropping rain the whole way! Can that much moisture really be in the clouds from the start, or are they continually reinventing themselves as they move along? I'll save that for a future stumper!

8 grams of liquid water (reducing my estimate) have a volume of 8 cm3 because the density of liquid water is about 1 gram / cm3. So how much of a cloud is actually water?

   8 cm3       8 cm3        8 cm3  
  -------- = --------- = ----------- = .000008
  1 meter3   (100 cm)3   1000000 cm3
Only a few millionths of the volume of a cloud is actually water. Water droplets don't usually collide.

The overall density of the water droplets in a cloud is less than the density of the air around them. Does that mean that a cloud floats because of bouyancy, like a cork in water? I don't think so. If I throw a handful of BBs into a large enough volume of air, it might be that the overall density of the BBs (as mass / volume) is less than the density of the air itself. But the BBs won't float because of it. A water droplet has a density of 1 g/cm3 no matter how small it is, so it's weight doesn't disappear, and it can only become negligible compared to some other force.

Does a floating cork still have a weight? (Of course!) Does an astronaut in freefall? (Uh...) Does a water droplet, or a dust mote, or a particle of smoke still have weight? This kind of ambiguity is a good reason to talk about mass instead of weight!

Why don't clouds fall? The accepted answer has to do with terminal velocity. Meteorologist H.C. Pumphrey explains like this:

The droplets are denser than the air around them and fall under the effect of gravity, but the viscous drag of the air prevents them reaching any great speed. Their downward velocity is usually much smaller than the upward velocity of the rising warm, wet air which created the cloud in the first place, so the cloud does not fall. If a droplet grows big enough, or enough of them stick together to make a larger droplet, then gravity will get the better of viscosity and the drop will fall as rain.
Terminal velocity or "viscous drag" depends on the surface area of an object (size squared). But mass depends on volume (size cubed). Mass becomes more important as things get larger. Cats and mice and beetles (in that order) survive a fall a lot better than I do!

Water droplets aren't exactly bouyed up by air, but I wonder if they're small enough to be bouyed up by electrical repulsion from the molecules of air around them. This would make a cloud a kind of colloidal suspension like milk or Jello, only it's a liquid suspended in a gas. Colloids typically involve particles in the nanometer range, and cloud droplets are larger, ranging from a few microns to a few tens of microns. On the other hand, I've seen plans for electrostatic fog machines, which suggests that electrcal forces are important, and of course lightning and rain come together.

I've been worried about our lack of rain this winter here in central California. Everything changed in February when we had 20 inches of rain at my home on San Marcos Pass. We were reported at the top of the rainfall charts on the Weather Channel! We even had 3 inches of snow last week (snow day!), fortunately not enough to damage our trees like last year. The Santa Ynez River is running high (fishing and tubing!), mushrooms are everywhere (chanterelles!), and I feel much better about next summer's fire season.

Snow day! Fishing and tubing! Chanterelles!

What happened to change our weather so suddenly this year? It's happened before. We had another March snow storm last year, and the "March Miracle" rains a decade ago saved us from an even worse drought. This is a real pattern, but why?

Here are a few Web links for more research about clouds.

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