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Finding the weight of water lost from cloud [Fluid Mechanics]

  1. Jan 18, 2016 #1
    1. The problem statement, all variables and given/known data
    The rain cloud has an approximate volume of 6.50 mile3and an average height, top to bottom, of 350 ft.1 mile = 5280 ft.
    If a cylindrical container 6 ft in diameter collects 2 in. of water after the rain falls out of the cloud, estimate the total weight of rain that fell from the cloud.

    2. Relevant equations
    1 mile = 5280 ft
    1 cubic foot of water = 62.4 lb
    6.5 mile3 = 9.57 * 1011 ft3

    3. The attempt at a solution
    Vcloud = (pi)(r2)(h)
    9.57 * 1011 ft3 = (pi)(r2)(350 ft)
    rcloud = 29498.4 ft

    2 in rain fell = 1.67 * 10-1 ft

    Vrain = (pi)(29498.4 ft)2(1.67 * 10-1 ft)
    Vrain = 4.57 * 108 ft3 water

    4.57 * 108 ft3 water * 62.4 lb/ ft3 water = 2.85 * 1010 lb of water.

    Does this seem correct? I have a habit of missing mundane details or sometimes the whole idea in general. Thanks for your help. -David
  2. jcsd
  3. Jan 18, 2016 #2


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    Seems correct. Might be an order of magnitude here or there, but operations are all present.
  4. Jan 19, 2016 #3


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    You've made the assumption that the cloud is a cylinder as well, which is not supported by the problem statement.

    Since you know the total volume of the cloud and the average height, you can find the area of the cloud which gives an equivalent volume of 6.5 mi3

    Once you do that, you can find out how many barrels would fit within this area, and knowing the amount of rain water collected in each barrel, calculate the weight of the rain from the cloud.
  5. Jan 19, 2016 #4


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    I think it's even easier than that.

    Once you have the area of the cloud just multiply by 2 inches to get volume of rain.
    (In the right units obviously).
  6. Jan 19, 2016 #5
    Okay so this is what I've come up with. The area of the cloud is equal to volume/height = 9.57 * 10^11 ft^3 / 350 ft = 2.73 * 10^9 ft^2

    Area of barrel = 28.3 ft^2
    Volume water in barrel = 4.72 ft^3
    Weight water in barrel = 294 lb
    Barrels that fit in area of cloud = 9.65 * 10^7
    Total weight = 2.84 * 10^10 lb

    Sorry for bad formatting I'm on my phone
  7. Jan 19, 2016 #6


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    CWatters idea is even simpler than this. :wink:
  8. Jan 19, 2016 #7
    So that sounds fine? That was my general idea in my first one I was just assuming the cloud to be a cylinder for some reason. Thanks for the help everyone. I'm still coming up with 2.84 * 10^10 lb so I guess I'll give that a shot.
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