anonymous
  • anonymous
A small dam is constructed across a stream. vertical cross section of the stream is y=2x^2. the dam is 4 ft tall. Set up and evaluate an integral that estimates the hydrostatic force on the damn when the water is all the way to the top. Force=Pressure*Area and Water weighs 62.5lb/cubic foot.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
here is a picture of the vertical cross section
anonymous
  • anonymous
Let's cut the water into n layers of thickness of x*subk, x being the kth level. The work done is Fx
anonymous
  • anonymous
ok

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anonymous
  • anonymous
i ended up with 471.4 lbs
anonymous
  • anonymous
I am trying to figure out the length across the top of the dam. Well, you already have an integral on your diagram, I am trying to set up an integral from scratch.
anonymous
  • anonymous
ok. the length across the top is \[2\sqrt{2}\]
anonymous
  • anonymous
r/x=sqrt2/4=1/2sqrt2
anonymous
  • anonymous
Getting lost
anonymous
  • anonymous
This is my hail mary: integral 0 to 4, (62.5pi/9)*4x^2 dx. Let's hope we're right or anyone on the other side is going to drown.
anonymous
  • anonymous
I'm sorry in place of 9 write in 2*sq rt 2
anonymous
  • anonymous
My buddy is a lecturer. He is in class right now. I'll call him later to see if we are on track.
anonymous
  • anonymous
I reserve the right to change integral 0 to 4 of 62.4(4-y) sq rt (2y) dy

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