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Math Help - A question about lbs of force

  1. #1
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    A question about lbs of force

    I am stumped, could anyone be of assistance?

    "What is the upward force on the bottom of an empty underground storage tank caused by a groundwater depth of 5 feet above the tank bottom? The tank is 8 feet wide and 16 feet long."

    Thanks!
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  2. #2
    A Plied Mathematician
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    Ok, so what is the physical picture here. What's going on? How would the groundwater exert an upward force on the tank?
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  3. #3
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    So we're talking weight to volume relations.
    What I know is 1 cubic foot of water weighs 62.4 lbs. One gallon of water weighs 8.34 lbs.

    So I suppose I need to figure out how much 5 feet of water weighs in a container that is 8x16 feet?
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  4. #4
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    Sounds good to me. You've got your Archimedean principle going here. The bouyant force is what is pushing up on the tank from below.

    What's the volume of water displaced by the tank?
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  5. #5
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    So I would take 5ft, and multiply it by 8ft (width of the tank) to establish that there is 40 cubic Ft of water. It would weigh 2497 Lbs and be 334 gallons. I'm still unclear on how to establish it's upward force.
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  6. #6
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    Quote Originally Posted by Greg999 View Post
    So I would take 5ft, and multiply it by 8ft (width of the tank) to establish that there is 40 cubic Ft of water. It would weigh 2497 Lbs and be 334 gallons. I'm still unclear on how to establish it's upward force.
    correction ...

    V = 5 \times 8 \times 16

    upward force is equal to the weight of the displaced water.
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  7. #7
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    Alright, so that gives me 640 for volume. Now that I've arrived at this number, how is the lbs of force established?

    This is multiple choice question, the options being 39,900 lbs, 43,300lbs, 49,900, 62,400 lbs, and 74,900 lbs.
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  8. #8
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    The trick now is to convert your volume answer into pounds of force. How do you normally do units conversion?
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  9. #9
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    Another approach is using pressure. The pressure at the bottom of the tank is given by:

    P = h\rho g

    where h is the depth of water,
    rho is the density of water,
    g the acceleration due to gravity.

    Then, we know that P = \frac{F}{A}
    where A is the area of the tank which is affected by the pressure, that is the bottom area of the tank,
    and F the force acting on the tank.
    Last edited by Unknown008; July 27th 2010 at 07:03 AM. Reason: added definition of F just in case.
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  10. #10
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    Hello,
    Don't complicate a simple problem.If the water is in the tank its weight is the upward force for water alone (tank weight excluded) When water is in the ground the pressure pushing up equals 5 ft of water. Answer is approx 40000 lbs 5x8x16x62.5


    bjh
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