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!

Conservation of mass/flow through tanks

  1. Sep 15, 2011 #1
    1. Suppose that three tanks in series, connected by pipes of the same size are filled with water that is moved through the system with pumps at the rate of 5 gal/min. The first tank is 1000 gal. The second tank is 750 gal. And the third tank is 500 gal. The contents of each tank is vigorously stirred. The in-feed to Tank 1 is a constant flow of water in the same sized pipe from an external source at the same flow rate and the outflow from Tank 3 flows into a lake at the same flow rate. [Dye is added to the inflow at a constant rate for exactly one minute per hour over a long period of time (weeks, months,whatever)]

    What is the concentration of the dye RELATIVE to its input concentration as a function of time over a 10-hour period after the "long-time" has passed.

    Do you have to make further assumptions to solve the problem?
    How do you deal with the "relative" concentration?




    2. Okay so obviously this is a conservation of mass problem, so flow in - flow out = 0



    3. I have drawn an accurate picture, and I have set up what I believe to be the correct system of equations:

    x1' = (QsA - Q12x1)*1/V1
    x2' = (Q12x1 - Q23x2)*1/V2
    x3' = (Q23x2 - Q3Lx3)*1/V3

    Where:
    x1 = Concentration in Tank 1, so on for x2 and x3
    A = Entrance rate of substance with units kg*t/v
    Q1 = rate at which the substance is transported by water flow (same throughout)

    V1 = Volume of tank 1, so on for V2, V3.

    Whatever you guys know what this stuff means these are straight forward normally but this one is throwing me off bad. I don't know if my system is right or what to solve I've been working on it and the rest of a huge problem set for too long.

    It is due tomorrow morning. Please help.

     
  2. jcsd
  3. Sep 17, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Well, input concentration is 100% for 1 minute and 0% for the next 59 minutes. So presumably you have to compute the concentration in each of the three tanks over the 1 hr period, second by second, after the steady state is reached.

    The concentration in each tank is probably represesnted by a first-order diff. eq. with constant coefficients. The forcing function is a square wave with 1/60 duty cycle. Sounds like a Fourier series application. If I think of any more brilliant suggestions I'll let you know, but probably too late ... :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Conservation of mass/flow through tanks
Loading...