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!

Calculating work done in draining water

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data

    http://imgur.com/BWo3tLh

    Using the fact that the weight of water is 62.5lb/ft3, find the work (in ft-lbs) required to pump the water out of the outlet when r =3ft. Make sure your answer is correct to within ten ft-lbs.

    2. Relevant equations



    3. The attempt at a solution

    I figured that Work is just force*distance, and force in this case is 62.5*V, while distance is just 3-height of the water, which i set as y

    I then get this equation for work

    62.5V(3-y)

    to find volume i wrote this as

    ∫62.5(pi)r^2(3-y) from y=-3 to y=0 bottom of hemisphere to top)which can be written as

    62.5pi∫r^2(3-y)

    I then tried to figure out a relationship between r and y, and i figured that because the hemisphere fit on the graph y=√(9-x^2) and then i plugged in r for x and rearranged it to give

    r=√(9-y^2)

    Then i put this back into the equation to finally get

    62.5pi∫(9-y^2)(3-y) = 62.5pi∫27-9y-3y^2+y^3

    After integrating i get 62.5pi(27y-9y^2/2-y^3+y^4/4)

    Then plugging in the points from -3 to 0 i finally end up with

    -62.5pi(-81-81/2+27+81/4) =~14579 ft lbs

    this is incorrect though.

    I feel like i may have used a wrong substitution for r, but i do not know how i can relate r and y. can anyone help?

    Thanks
     
  2. jcsd
  3. Jan 31, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are saying height=(3-y). If y=(-3) at the bottom and y=0 at the top, does that really work? That would say height=6 and the bottom and height=3 at top. Doesn't seem right.
     
    Last edited: Jan 31, 2013
  4. Jan 31, 2013 #3
    oh i see. I forgot to change that when i was trying to do it another way previously. Thanks for the help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calculating work done in draining water
  1. Work to drain a tank (Replies: 1)

Loading...