1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Emptying a tank of oil

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data
    A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot. Find the work required to pump oil out through a hole in the top of the tank.

    3. The attempt at a solution
    this is an example problem in my book and they start off by subdividing the region into disks of thickness Δy and radius x and by saying as a result of the increment of force for each of these disks being given by weight we have ΔF = weight → (50pounds/ft3)*volume → 50(∏x2Δy)pounds. This is where I get stuck, I have no idea where that expression, ∏x2Δy, came from. Are they using ∏r2h here for the volume of each cylindrical shell?
     
  2. jcsd
  3. Apr 2, 2013 #2
    Well if you're cutting the sphere in many pieces horizontally, you get circles, right? So the area of one of these circles is πx2. The thickness of the circle is Δy. So with all that you can plug it into the integral for work.
    Edit: Forgot to add, the radius is changing at certain spots right? So you have to take that into account.
     
  4. Apr 3, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    As iRaid said, for each different level, y, we have a disk of oil with radius x, so area [itex]\pi x^2[/itex]. Further, the thickness of each disk is [itex]\Delta y[/itex] so its volume is [itex]\pi x^2\Delta y[/itex]. Finally, you multiply by the density to get the weight, [itex]50\pi x^2\Delta y[/itex], to get the weight that will be lifted to the top of the tank. That weight, times the height lifted, gives the work done in lifting that disk of oil to the top of the tank. Suming over all "disks" gives a Riemann sum approximating the work done lifting all of the oil. Convert that Riemann sum to the integral that gives the exact value.
     
  5. Apr 3, 2013 #4
    alright thanks a lot everyone. Got it now.
     
    Last edited: Apr 3, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Emptying a tank of oil
  1. Empty set? (Replies: 1)

  2. Empty Conical tank (Replies: 0)

  3. Draining a Tank (Replies: 5)

Loading...