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Differential Equation with growth

  1. Nov 12, 2012 #1
    So, I have a differential equation with growth problem. It is a dm/dt function and I need to get it to dD/dt, change in diameter with time.

    here is the original functon,
    dm/dt= (pi/4)(D)^2* (V(D))*(LWC)*E

    E=1
    LWC = 2
    V(D) = 343D^0.6 m/s

    it starts from a diameter of 1mm and grows to 5mm and I need to find the time it takes.

    I'm not asking for anyone to solve the problem and give me a final solution, but I need help in getting the dD/dt function.

    I thought this was it.... but its not:
    multiplying by dt ___ dm = [(pi/4)(D)^2 * (v) * (LWC) (E)] dt

    integrating ___ m = [(pi/4)(D)^2 * (v) * (LWC) (E)] t

    dividing ___ m / [(pi/4)(D)^2 * (v) * (LWC) (E)] = t


    thanks
     
  2. jcsd
  3. Nov 13, 2012 #2

    HallsofIvy

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    I don't see how you can possibly change from dm/dt to dD/dt without knowing how m is related to D.
     
  4. Nov 13, 2012 #3
    m=(pi/6)(density)(D^3)
     
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