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anonymous

  • 5 years ago

a small dam is constructed across a stream. a vertical cross section of the stream is y=2x^2. The dam is 4 ft tall. set up an integral that estimates the hydrostatic force on the dam when the water is all the way at the top. Force=Pressure*Area. water weighs 62.5 lb/cubic foot

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  1. anonymous
    • 5 years ago
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    so far i have \[\int\limits_{0}^{4}62.5 \] i need help with coming up with the Area part of the integral to be evaluated

  2. anonymous
    • 5 years ago
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    so far i have \[\int\limits_{0}^{4}62.5 \] i need help with coming up with the Area part of the integral to be evaluated

  3. dumbcow
    • 5 years ago
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    i think you need to find the area of the horizontal cross section since you're integrating from 0 to 4. get x in terms of y -> x = sqrt(y/2) do we know how wide the stream is?

  4. anonymous
    • 5 years ago
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    thats what i thought too but i l looked up the definition of vert. cross section and it said from teh side so it makes sense. i think the width of the stream is dx since it changes with the depth of the water, looking at the vertical cross section.

  5. anonymous
    • 5 years ago
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    ill take a picture and attach what ive drawn

  6. anonymous
    • 5 years ago
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  7. dumbcow
    • 5 years ago
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    ok the area of the inside of the parabola is sum of 2*x distance * dy ->x = sqrt(y/2) ->area = integral 2sqrt(y/2)dy so add that to integral above,

  8. anonymous
    • 5 years ago
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    i got \[\int\limits\limits_{0}^{4}62.5*2x^{2} dx\] using dx as the width of the estimating rectangle and \[y=2x^{2}\] as the height of the estimating rectangle but you're saying it's \[\int\limits_{0}^{4}62.5*2\sqrt{y/2}dx \] ?

  9. dumbcow
    • 5 years ago
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    correct except its dy not dx i get an answer of 471.39

  10. anonymous
    • 5 years ago
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    why is it dy?

  11. dumbcow
    • 5 years ago
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    because we are integrating from 0 to 4 which is the height or y value imagine that 2sqrt(y/2) is width of a rectangle and dy is the height

  12. anonymous
    • 5 years ago
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    yea im just having trouble getting the equation from the problem. F=Pressure*Area and I got the pressure because it was given and im not understanding what makes up the Area part of the equation

  13. anonymous
    • 5 years ago
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    oh ok. x=width and dy is the height because its changing

  14. dumbcow
    • 5 years ago
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    correct

  15. anonymous
    • 5 years ago
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    thanks!

  16. dumbcow
    • 5 years ago
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    its backwards a little bit. ok your welcome

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