12022004, 04:11 AM  #1 (permalink) 
Insane
Location: West Virginia

Cannot figure out this calculus problem at all!
Okay...
A cylinder is given, laying on its side. It is 6 feet long, and has a 3 feet diameter. There is a pipe coming into the cylinder one foot above the top of it and extending to the bottom to pump out water. Given F = 9.8 * 1000, what is the work required to pump all of the water out? Remember, its laying on its side... so the height is the diameter. What I tried was the following: Integral from 0 to 1.5: (2)(9800)(4x)^2(pi)(6)dx Which comes out to 9800(126pi) This is incorrect. I have the answer which is supposed to come out to 9800(33.75pi) Thanks for any help =)
__________________
 Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know 
12022004, 10:16 AM  #5 (permalink) 
Insane
Location: West Virginia

"There is a pipe coming into the cylinder one foot above the top of it and extending to the bottom to pump out water."
It doesn't take work to life the water over the 3 foot wall of the cylinder?
__________________
 Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know 
12022004, 10:59 PM  #7 (permalink) 
Insane
Location: West Virginia

Now I have it set up like..
The integral from 0 to 3 of: 9.8*1000*6*(x+1)*(2*sqrt(2.25x^2)) You can distribute the x+1 into two integrals but I cannot get this to solve correctly :/
__________________
 Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know 
12032004, 03:02 AM  #8 (permalink)  
Likes Hats
Location: Stockholm, Sweden

Quote:
At every lecture he'd mock some poor student who had made a stupid error on one of his exams. We all lived in mortal fear of becoming one of his examples. 

12032004, 05:02 AM  #9 (permalink) 
Insane
Location: West Virginia

Work is force x distance, if that's what you need to know. And yes, even with a siphon there is work being done  by the siphon. As for the hose comment, the pipe enters the cylinder from a height one foot above the top. Meaning it has to lift the water 1 extra foot past the top of the cylinder before it can exit.
But before we get too far off topic  let me just say that I figured this out. I had to take the integral from 1.5 to 1.5 and use 2.5  x for the height of the pipe for any who was wondering.
__________________
 Artsemis ~~~~~~~~~~~~~~~~~~~~ There are two keys to being the best: 1.) Never tell everything you know 
Tags 
calculus, figure, problem 
Thread Tools  

