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Math Help - trapezoidal section

  1. #1
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    trapezoidal section

    Evening all.

    Im getting stuck on a question that I just cant figure out.

    I'll relay it below and if anyone could offer some help it would be much appreciated.

    A cooling tank is to be made with a trapezoidal section as shown below. Calculate for a minimum width W, the material needed to form the bottom and folded sides.

    45° \_CSA=300000mm2_/ 45°
    ¦<---- W --------->¦

    Hope the crude drawing works but all I have is a CSA and the angles of the sides. Many thanks
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  2. #2
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    Quote Originally Posted by haverford View Post
    Evening all.

    Im getting stuck on a question that I just cant figure out.

    I'll relay it below and if anyone could offer some help it would be much appreciated.

    A cooling tank is to be made with a trapezoidal section as shown below. Calculate for a minimum width W, the material needed to form the bottom and folded sides.

    45° \_CSA=300000mm2_/ 45°
    ¦<---- W --------->¦

    Hope the crude drawing works but all I have is a CSA and the angles of the sides. Many thanks
    I'm not certain that I understand your question correctly but I'll give it a try:

    1. I assume that you are asked to minimize the material used to form the bottom and the 2 slanted sides of the tank. If so:

    Let L denote the complete length (2 slanted sides and the bottom):

    L = w + 2s

    2. The cross section of the tank consist of a rectangle and a square which is formed by the two right isosceles triangles:

    s = h \cdot  \sqrt{2}

    a = w \cdot h + h^2

    With a = 300,000 mm˛ you get: w = \frac{300,000-h^2}h

    3. Plug in these terms into the equation of L:

    L(h)= \frac{300,000-h^2}h + 2 h \sqrt{2}

    4. Differentiate L wrt h and solve the equation L'(h) = 0 for h.

    5. Plug in the calculated value of h into the equation of w.

    6. For confirmation only: I've got w = 335.56 mm
    Attached Thumbnails Attached Thumbnails trapezoidal section-trapeztank.png  
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  3. #3
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    thank you very much for your help
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