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!

Mixing Differential Equation - need confirmation of the process.

  1. Mar 22, 2007 #1
    Mixing Differential Equation -- need confirmation of the process.

    1. The problem statement, all variables and given/known data

    There is a box with 320 cubic feet of air mixed with .2 pounds of some some impurity. A small ventilation fan is added to the box at one end. Find the flow rate (R) of the fan as such that no more than .0002 pounds of impurities remain in the box after 4 hours.

    Variables:
    I = the amount of impurities remaining in the box in pounds - @ t = 0, I = .2; @ T=4, I = .0002

    R = the flow rate of the fan in cubic feet per hour- unknown must be solved for.

    3. The attempt at a solution
    My assumption is that: ( units are in brackets)
    [tex]\frac{dI}{dt} = 0 - R \frac{ft^3}{h}* \frac{I(t)}{320} \frac{lbs}{ft^3} = - R * \fracI(t)}{320} \frac{lbs}{h}[/tex]

    This equation now can be integrated to find:
    [tex]I = .2 e^{-\frac{R}{320} T}[/tex]

    Next we plugin the T we have and the impurities (I) at time t, and we get the flow rate of R = 552.62

    Up until this point is the work and logic correct?
     
    Last edited: Mar 23, 2007
  2. jcsd
  3. Mar 23, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, it looks good.
     
  4. Mar 23, 2007 #3
    Thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mixing Differential Equation - need confirmation of the process.
Loading...