## anonymous 5 years ago 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.

1. anonymous

here is a picture of the vertical cross section

2. anonymous

Let's cut the water into n layers of thickness of x*subk, x being the kth level. The work done is Fx

3. anonymous

ok

4. anonymous

i ended up with 471.4 lbs

5. 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.

6. anonymous

ok. the length across the top is $2\sqrt{2}$

7. anonymous

r/x=sqrt2/4=1/2sqrt2

8. anonymous

Getting lost

9. 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.

10. anonymous

I'm sorry in place of 9 write in 2*sq rt 2

11. anonymous

My buddy is a lecturer. He is in class right now. I'll call him later to see if we are on track.

12. anonymous

I reserve the right to change integral 0 to 4 of 62.4(4-y) sq rt (2y) dy