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Homework Help: Horizontal force on one side

  1. Jun 14, 2008 #1
    A square tank 12 feet high having a perimeter of 40 feet is filled with water weighing 62.4 pounds per cubic foot. The total horizontal force on one side of the tank due to the water pressure is MOST NEARLY ________ pounds.

    A. 58,000
    B. 45,000
    C. 36,000
    D. 13,000

    The answer key says 45,000 lbs. is the answer but I have no clue how they got there.
    Total pressure - lbs./ft^2 - should be 12 x 62.4, or 5.2lbs/in^2. How do they get 45,000?
  2. jcsd
  3. Jun 14, 2008 #2


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    First: what is the volume of the tank? Note that 40 feet is the perimeter. Secondly, how do you calculate the horizontal force given the volume of water and the weight (look in your text book or lecture notes)
  4. Jun 14, 2008 #3
    Square Tank

    with perimeter 40 feet. So each side is 10 feet. I really am mildly ashamed to admit that I don't recall a formula for "horizontal" pressure. I thought pressure at the same depth was the same throughout a fluid. This question is for a State Civile Service exam. NY State. Maybe we do things differently.
  5. Jun 14, 2008 #4


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    Hi jbowers9! :smile:

    Yes, pressure is the same in all directions at any fixed height.

    Hint: force = pressure times area.

    And how does the pressure change with the depth? :smile:
  6. Jun 14, 2008 #5
    Horizontal Pressure


    So the area of the tank is 100ft^2...
    It's 12 ft high...
    62.4 x 10 X 10 X 12 gives total force which is not 45,000 lbs.
  7. Jun 14, 2008 #6


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    urgh! :yuck:

    That's the mass! :cry:

  8. Jun 16, 2008 #7
    Horizontal "Force"

    Actually, the density x volume IS the force in the English system. Lbs. is a measure of force (mass x g). The English system of mass is the slug.
    I figured it out Saturday evening. 62.4y - if y is the verticle coordinate - is the PRESSURE at any depth y in the tank (lbs/ft^2). 10dy is an element of area along one side of the tank.
    642 y dy integrated over the limits 0 - 12 give 642 x 72 = 46,224 which is close enough to the given answer of 45,000 for me. Notice that the dimension of the answer is pounds. Which is a unit of FORCE in the English system. Thank you.
    Last edited: Jun 16, 2008
  9. Jun 17, 2008 #8


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    Hi jbowers9! :smile:
    I did know that! :smile:

    But the mass (in pounds) is a vertical force, and you were asked for the horizontal force! :rolleyes:
    erm … I think you'd get a lot closer if you used 624 instead of 642. :smile:
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