How Much Water in a Cloud?

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I have recently been wondering about the weight of water in a typical cu-nim.

I suspect there's information out there about water density in the various types of cloud, because engine makers, among others, need to know that. But I can't find it.

Does anyone know the answer? I'm interested only in an approximation, not a scientifically robust calculation...

Take a fairly typical West European cu-nim, for example, let's say from 2,500 to 35,000 at the anvil, perhaps 5 km average diameter at the base, normal kind of shape and development. That's my uneducated guess at typical dimensions from observation from the ground and from the air, either in a light aircraft and avoiding it, or looking down on one from a civil airliner. Perhaps they are totally wrong. Anyone know?

What's the tonnage of the water that's held suspended by that cloud?

[Mad (Flt) Scientist]

Appendix C of Part 25 has data regarding liquid water content of clouds for the purpose of icing analysis. While this is obviously a subset of clouds, it'll do for a rough guess.

The continuous maximum conditions probably have an average LWC of 0.5 g/m^3 or less (its a function of air temp, assumed droplet size, and cloud size). Your cloud is about 10km tall and 5km diameter - that's a volume of roughly 200,000,000,000 cubic metres (as a cylinder) - which would be 100,000,000,000 grams, or 100,000 tonnes.

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Even if one assumes that the shape gets narrower with height, not necessarily the case, that's 60,000 - 75,000 tonnes.

There's only one thing to say.

"Gorblimey, thatsa helluva lot of water.."

Thanks.

[Mad (Flt) Scientist]

There's a rather more silly example here - silly in the sense that they use "elephants" as a unit of measure.

Converting back to "real" units:

For a small cumulus : 550 tons
"a big storm cloud" : 1 million tons
"hurricane" : 250 million tons

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Well, I'm not alone in my astonishment.....

But still, the concept of so much water floating in the sky was surprising even to a meteorologist like LeMone.

"I had no idea how much a cloud would weigh, actually, when I started the calculations," she says.

And if "a big storm cloud" is what my example of a "typical cu-nim" is, it's 10 - 16 times as much as we thought, if she's right.

What I cannot imagine are the forces needed to hold 1,000,000 tonnes of water suspended in that relatively small area.

I can't think in elephants like LeMone, but if I've got it right, 1,000,000 tonnes of water is going to be 1,000,000 cubic metres of water. That's a block of water 100m long, 100m wide, and 100m high.

I can think in ships, though...that's the gross weight of 6 and 2/3rds Queen Mary IIs.

Oh, alright, 157,000 adult African elephants, give or take a few. (I think LeMone is working in Indian elephants. They're thinner and smaller, you know, but then so are the Indians.)

Imagine them poised above your head, supported on rising air, next time a cu-nim passes over the house!

[wiggy]

Chuffin 'eck, what a great question and as for the answer.... I'm gobsmacked. I'd best invest in a stronger umbrella and a hard hat.

[Mad (Flt) Scientist]

Well, since water vapour is actually less dense than standard air, you really need that hard hat more when there's a clear sky ....

[rsuggitt]

Another way to go at the calculation is to work on the basis that a storm might dump 2cm of rain in a nomial circular area of 5Km radius. I make that 1.5 million tonnes.

[Mad (Flt) Scientist]

Puts somewhat into context all the numbers of tonnes of CO2 bandied around with regard to aircraft emissions etc., doesn't it?

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Well, since water vapour is actually less dense than standard air, you really need that hard hat more when there's a clear sky ...

I think I sense the beginnings of a glimmer of an understanding about why the stuff stays up there even though it weighs 157,000 elephants; would that be right?

[Mad (Flt) Scientist]

It would indeed.

All gases have the same volume per mole (which is a staggeringly huge number of molecules). Therefore the density of a gas is directly related to the weight of one molecule of the gas, since the same number of molecules fit in the same volume, regardless of the gas.

Water, H2O, has a atomic weight of 18 (1 each for hydrogen, 16 for oxygen)

Air is a mixture of various gases, but mainly Nitrogen (N2, atomic weight 28) and Oxygen (O2, atomic weight 32), and the average for air is about 29.

Therefore water gas (vapour) is only 18/29th the desnity of air, under similar conditions. So even if some water vapour condenses to very small droplets, the density of the resulting cloud will not be dissimilar to air, so it will float.

[rsuggitt]

"Therefore water gas (vapour) is only 18/29th the desnity of air, under similar conditions. So even if some water vapour condenses to very small droplets, the density of the resulting cloud will not be dissimilar to air, so it will float."

Water vapour is not the same as cloud. Cloud is liquid water droplets that have condensed out from vapour. Now for them the important bit of physics is how fast do they fall compared to the speed of the updraft that lofted the water-vapour-bearing-air and cooled it to dewpoint. Reynolds number plays a significant part due to small droplet size.

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Oh God, now we're back to the forces (updrafts) needed to keep 157,000 elephants airborne in a quite small patch of sky.

Just when I thought I had it sussed.

The same forces (yes, I know, as well as things like waves) keep the gliders up. But 157,000 elephants, with nothing to help apart from low aspect ratio ears and Reynold, are a different proposition. Aren't they?