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!

Diff. Eqs. Mixing Problem

  1. Jan 29, 2007 #1
    I haven't found any examples anywhere on how to do a mixing problem where you don't know the rate of volume change, could someone give me a hand just setting up the equation? Here is the problem. . .

    1. A tank contains 500 gal of a salt-water solution containing 0.05 lb of salt per gallon of water. Pure water is poured into the tank and a drain at the bottom of the tank is adjusted so as to keep the volume of solution in the tank constant. At what rate (gal/min) should the water be poured into the tank to lower the salt concentration to 0.01 lb/gal of water in under one hour?
     
  2. jcsd
  3. Jan 29, 2007 #2
    Sorry I didn't post what work I've tried:
    if x(t) is amount of salt in that tank then
    dx/dt=Volume in*Salt Concentration in-Volume out*Salt Contentration out
    dx/dt=Volume in*(0)-Volume Out*(x/500)
    dx/dt=-(x/500)*(Volume Out)
     
  4. Jan 29, 2007 #3

    Pyrrhus

    User Avatar
    Homework Helper

    Hey there, in the beginning before pumping out the salt (x(0)=25 lb), you know the tank will have 25 pounds of salt dissolved, then you want to diminish that to 5 pounds of salt (x(t) = 5 lb). You are given the time too, so t = 60, if the time is in minutes.
     
    Last edited: Jan 29, 2007
  5. Jan 30, 2007 #4
    Ok, maybe I'm missing some obvious thing but does the information you gave let me calculate dx/dt? I'm still confused. I was pretty sure I'd use that information after I had calculated the differential equation.
     
  6. Jan 30, 2007 #5
    You're looking for volume/time at time t where salt concentration =.01, essentially what it's asking you to do is to rearrange the equation so that the unknown is = to the variables you are given, have a play around untill you find an equation that relates pounds and time to volume

    Once you have that you should be able to integrate to find your answer. at f'(59.59) t=59.59 or just under an hour where salt concentration=.01.

    ie with these values of the variables in your equation with the unknowns (x) etc.

    EDIT: Sorry I meant integrate obviously.
     
    Last edited: Jan 30, 2007
  7. Jan 30, 2007 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    And "Volume Out" is the constant you want to find: call it v.

    dx/dt= -(v/500)x

    Can you integrate that? What must v be so that x(1)< 0.01?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Diff. Eqs. Mixing Problem
Loading...