1. Limited time only! Sign up for a free 30min personal 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!

Interesting problem

  1. Dec 14, 2009 #1
    There is a popular myth that after drinking a bottle of water, the last bit is mostly backwash. Well I decided to try and test it, but got stumped.

    Lets call y the amount of backwash in the bottle
    Lets call x the number of sips taken
    The volume of the bottle will be 1000mL
    Assume each sip is 20mL
    Assume that each sip backwashes 0.05mL into the bottle

    dy/dx= 0.05 -20( y / (1000 -(20-0.05) x ) )

    I can't separate variables here, so I do not know what to do. This is not a homework problem, I was just wondering if anyone could help me solve this differential equation. At 51 sips there will be nothing left in the bottle.
     
  2. jcsd
  3. Dec 14, 2009 #2

    diazona

    User Avatar
    Homework Helper

    I tinkered with it a bit... try making the change of variables [itex]x' = 1000 - (20 - 0.05)x[/itex], then look at http://en.wikibooks.org/wiki/Differential_Equations/Exact_1 [Broken]. I didn't take the calculation all the way through but it looks solvable that way.
     
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...