Results 1 to 4 of 4

Math Help - Emptying Tanks Modelling with Euler's Method

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    26

    Emptying Tanks Modelling with Euler's Method

    I'm doing a practice paper for a past mathematical modelling exam. I've attached the problem

    What I'm having trouble with is simplifying the equations and variables into a differential equation that is solvable with Euler's Method.

    What I have currently is the sqrt(h1-h2) in the equation which leads to an imaginary number so I don't think I have done it correctly. ( As h1<h2..I think the diagram is also misleading)

    If someone could help me out with getting the right equation I should(hopefully) be able to do the next part.

    The second question doesnt need to be attached, it is:
    Use Euler's method to make a single step to predict the levels in both tanks after 5 seconds.

    Thanks
    Attached Thumbnails Attached Thumbnails Emptying Tanks Modelling with Euler's Method-questionpart1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jul 2006
    Posts
    364
    I may be wrong, but all you are looking for is an autonomous system:

    \frac{\text{d}h_1}{\text{d}t} = f(h_1, h_2), h_1(0)=0.6

    \frac{\text{d}h_2}{\text{d}t} = g(h_1, h_2), h_2(0)=0.85

    So, divide through by \rho and do a bit of algebra, and you get

    f(h_1,h_2) = 18-\frac{\sqrt{h_1-h_2}}{100} and

    g(h_1, h_2) = \frac{1}{100}(\sqrt{h_1 -h_2}-2\sqrt{h_2})

    where t is in hours,

    Then pick step size h = 5/3600 to step in units of 5 seconds.

    Edit: I messed up the units here -- so my equations are definitely wrong. Sorry
    Last edited by scorpion007; October 22nd 2009 at 09:40 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    26
    As far I can see that still takes the square root of a negative number?

    sqrt(h1-h2) or sqrt(0.6-0.85)??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2009
    Posts
    26
    I've attached what I got but not sure how to solve with the square root of negative number so guessing its wrong as well?

    Edit: should be a subscript 2 not h_2
    Attached Thumbnails Attached Thumbnails Emptying Tanks Modelling with Euler's Method-equations.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euler method
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 11th 2011, 04:59 AM
  2. Euler's method
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 8th 2010, 04:48 PM
  3. Euler Method
    Posted in the Math Software Forum
    Replies: 5
    Last Post: March 15th 2009, 02:58 PM
  4. Euler's Method
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: March 4th 2009, 06:19 AM
  5. Euler's Method
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: July 20th 2007, 10:07 AM

Search Tags


/mathhelpforum @mathhelpforum