What is the volume of water in a cylindrical cumulus cloud of given dimensions?

[scmejla]

Does the solution to this problem look right?

A cubic centimeter in a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 µm. For that range, give the lower value and the higher value, respectively, for the following.
(a) How many cubic meters of water are in a cylindrical cumulus cloud of height 3.6 km and radius 1.1 km?

Vdrop = 4/3 * pi * (10^-6 m)^3 = 4.18879(10^-15) m^3

Vdrop*50 = 2.0944(10^-13) m^3/(10^-2) m^3 = 2.0944(10^-11)
Vdrop*500 = 2.0944(10^-12) m^3/(10^-2) m^3 = 2.0944(10^-10)

Vcloud = pi * 3.6(10^3) m * (1.1(10^3) m)^2 = 1.36848(10^10) m^3

Lower value = 2.0944(10^-11) * 1.36848(10^10) m^3 = 0.286614 m^3
Higher value = 2.0944(10^-10) * 1.36848(10^10) m^3 = 2.86614 m^3

 

[saltydog]

Does the solution to this problem look right?

A cubic centimeter in a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 µm. For that range, give the lower value and the higher value, respectively, for the following.
(a) How many cubic meters of water are in a cylindrical cumulus cloud of height 3.6 km and radius 1.1 km?

Vdrop = 4/3 * pi * (10^-6 m)^3 = 4.18879(10^-15) m^3

Vdrop*50 = 2.0944(10^-13) m^3/(10^-2) m^3 = 2.0944(10^-11)
Vdrop*500 = 2.0944(10^-12) m^3/(10^-2) m^3 = 2.0944(10^-10)

Vcloud = pi * 3.6(10^3) m * (1.1(10^3) m)^2 = 1.36848(10^10) m^3

Lower value = 2.0944(10^-11) * 1.36848(10^10) m^3 = 0.286614 m^3
Higher value = 2.0944(10^-10) * 1.36848(10^10) m^3 = 2.86614 m^3

Hello Scmejla. Interesting problem. You know that's a big cloud but you're saying it has only .2 m^3 of water. That's only a few buckets full. Surely it has more than that, few truckloads at least. I checked your work. You calculated volume of water in a drop (in cubic meters). That's 4.18*10^-15. For the lower limit, there are 50 of those drops in every centimeter and 1 million cubic centimeters in a cubic meter. Thus, the low limit of the amount of water in 1 cubic meter is how much?

Edit: Alright, maybe 10 or 12 you know what I mean. So how many bucket-fulls of water are in .28 m^3? You know, without calculating it, I'd guess now around 15. I say we figure how many bucket-fulls of water are in that cloud anyway.

 

[scmejla]

Thanx for setting me straight, I should have realized that was an awful small amount for such a big cloud.