I’m watching the rain clouds loom overhead and it has me wondering. Is it possible to put a range of numbers onto a cloud? I know there are different sizes, but let’s consider this an average sized cloud that holds the maximum capacity of water before it bursts and sends showers down to the earth.
So, depending on the temperature, air in a nice warm cloud could certainly include more than a percent by mass of water. Air weighs a kilogram per cubic meter, and one percent of that is 10 grams per cubic meter. If a cloud is as big as a kilometer cube, or a billion cubic meters, that would be ten billion grams of water, or ten million liters of water. If the raindrops are the volume of a 3 mm cube, or 30 mm^3, there are 0.03 of them in a cubic millimeter, or 30 in a cubic centimeter, or 30,000 of them in a cubic decimeter or a liter. So that’s 3E10 drops in the cloud.
Of course, the pedantic answer is that there are no raindrops in a cloud, merely droplets. Once enough droplets have combined to form a raindrop, it falls out of the cloud. So, maybe there are a few transition state drops, but not many. Your question really is one more of how many potential raindrops are in a cloud?
Can we start these calculations over? 2.2 lbs per cubic meter? Air? Nope.
By way of comparison, an Olympic pool (25 X 50 X 2 meters) contains two point five million liters of water.
Interesting calculations so far… I’m not too big of a math person so I have to mull it over a bit. Does it matter what the air is comprised of? I mean, I know - oxygen… but what if I were in a nitrogen or CO2 heavy atmosphere? Would that affect the chemistry of rain clouds (ie acid rain heavier than normal rain?) and thus the number of droplets a cloud contains before release?
Some clouds contain ice, not liquid water. Wouldn’t that make a difference in volume?
The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth’s atmosphere, and is a useful value in aeronautics. Air density decreases with increasing altitude, as does air pressure. At sea level and at 20 °C, air has a density of approximately 1.2 kg/m3."
muldoonthief already got to it, but the misconception here is probably that a one meter cube balloon doesn’t weigh any more than the same deflated balloon. This is because the pressures are the same on the inside and outside (otherwise, the balloon would equilibriate to a different size), making the force of gravity canceled out by the buoyant effect of the air under the balloon. 1 kg per m[sup]3[/sup] is a commonly accepted estimation for back of the envelope calculations (it’s the density I used when calculating the drag due to air resistance in the paddle with holes thread.)
If we’re going to be pedantic, we would say that not all raindrops start falling from the very bottom of the cloud. Ones that start falling from near the top would certainly be defined as being in the cloud at a snapshot in time.
Could we go with “nearly the same” ? Otherwise, the air wouldn’t rush out of the balloon when you let go of the neck.
If we’re talking about sea level and 20 degrees C, you are quite right to question this figure - the correct value is 2.6 lbs per cubic meter.
(IOW, air has a higher density than many people assume.)
You are in a nitrogen heavy atmosphere.
- 78% nitrogen
- 20% oxygen
- 2% and the rest
Good point. I glossed over the force the elastic was exerting. “Nearly the same” it is.