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Problem of a tank with trapezoidal section.

  1. Aug 22, 2015 #1
    1. The problem statement, all variables and given/known data
    A deposit of 20 feet long and 10 feet high, has a width of 8 feet at the bottom and 18 feet at the top. In the bottom is an orifice an area of 24 in2 and discharge coefficient of 0.60. If the tank is full calculate the time required for the lower level 6 feet. Consider full contraction of the jet.



    2. Relevant equations
    upload_2015-8-22_19-29-33.png

    a= area of the orifice
    c= discharge coefficient


    3. The attempt at a solution
    I have found a relationship between the variable X (width) and the variable H (height). I prolongate the sides of the trapeze until have a triangle. 18 / 8 = Y / (Y-10), where Y is the height from the vertix of the triangle to the bottom of the triangle. So I have that Y=18 ft. After that I did another relation of triangles: x/18 = H/(Y=18)-------x=H

    I applied the diferential equation dt= 24.922 H ^(1/2) dH; with height limits from 18 feet to 14 feet.



    But I dont know if it's right or not
     
  2. jcsd
  3. Aug 22, 2015 #2
    Show us your equation for A(h).

    Chet
     
  4. Aug 22, 2015 #3
    I have surface area =20 H, because the lenght of 20 is constant. And from the relation between triangles I know that X=H
     
  5. Aug 23, 2015 #4

    haruspex

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    The width increases by 10 ft as the height increases by 10 ft, but you can't set h=0 at 8 feet below the base of the container. That would make your ##ac\sqrt{2gh}## wrong.
     
  6. Aug 23, 2015 #5
    I get 20(8+h).
     
  7. Aug 23, 2015 #6
    I think I understand, but there are some exercises in which is valid to take the zero down or away from the element considered. For example in this exercise (strain energy) and I only integrate in the real part of the element. So when will know whether it is valid or not take away the element origin?

    upload_2015-8-23_9-9-54.png

    upload_2015-8-23_9-11-30.png
     
  8. Aug 23, 2015 #7
    Thank you, I got this too, when I put the origin in the base of the tank
     
  9. Aug 23, 2015 #8
    I got this by just fitting a straight line between between (0,8) and (10,18).

    Chet
     
  10. Aug 23, 2015 #9

    haruspex

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    It's valid as long as you are consistent. Your problem was that in different equations you were measuring h from different origins.
     
  11. Aug 23, 2015 #10
    Thank you
     
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