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Equation for time?

  1. Nov 14, 2012 #1
    1. The problem statement, all variables and given/known data
    How do you differentiate this to get a change in time equation?

    we have:
    (dm/dt) = (pi/4)(D^2)(V(D))(LWC)(E)

    LWC = 2E-6
    E=1

    these two values aren't important until the very end when finding the actual time, just a plug and chug then. I'm having trouble solving for Δt!
    need to get (delta t) so find the time.


    2. Relevant equations

    this is what we're looking for : Δt = ?



    3. The attempt at a solution
    (dm/dt)= (row)(pi/6)(3D^2)(dD/dt) = 343(pi/4)(D^2.6)(LWC)(E)
     
  2. jcsd
  3. Nov 14, 2012 #2

    Mark44

    Staff: Mentor

    This is very unclear. In fact, I am completely mystified by it.
    For starters, you wouldn't differentiate this, since what you have already is a derivative.
    To continue, you have a bunch of letters whose meaning you don't give. Are they variables? Do D and V(D) depend on t?

    If E = 1 does it mean that LWC = 2*1 - 6 = -4?
    Or are you writing 2 X 10-6?
    What is "row" and where did it come from? Do you mean the Greek letter "rho" (## \rho##)?

    How did (dm/dt) = (pi/4)(D^2)(V(D))(LWC)(E) change to (dm/dt)= (row)(pi/6)(3D^2)(dD/dt) and how is this equal to 343(pi/4)(D^2.6)(LWC)(E)?

    Finally, if E = 1, why is it still being dragged along?
     
  4. Nov 14, 2012 #3
    "(dm/dt)= (row)(pi/6)(3D^2)(dD/dt)=343(pi/4)(D^2.6)(LWC)(E)"

    is directly from my instructor.

    yes, I meant "rho".

    this is for graupel growth. trying to find out how long it takes for a 1mm piece of graupel to grow to 5mm.

    The original equation is (dm/dt)=(pi/4)((D)^2)(V(D))(LWC)(E)

    D= diameter
    LWC = liquid water content = 2 x 10^-6 g/cm^3
    E = 1.0
    rho = 0.6 g/cm^3
     
  5. Nov 14, 2012 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    You never really answered Mark his questions, so I'll ask them again:

    How does (dm/dt)= (row)(pi/6)(3D^2)(dD/dt)=343(pi/4)(D^2.6)(LWC)(E) change to (dm/dt)=(pi/4)((D)^2)(V(D))(LWC)(E)?

    Do any of the variable D, LWC, V and other depend on t?

    Why would you differentiate something if you're already given a derivative??

    Why drag E along if E=1?

    Can you present us with the exact problem description as it is given to you??
     
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