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Mass Continuity Equation Problem

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Question Details:

    The question reads:

    Show that the equation:

    dA/A + dv/v + dρ/ρ = 0

    applies to a one-dimensional steady flow. (Here 'one dimensional' means that both the density ρ and seed v = - v . n (vectors) are constant across any cross-sectional area A cutting the flow.)

    Please help!

    2. Relevant equations

    d/dt ∫V ρ dV + ∫A -ρv⋅n dA = 0

    3. The attempt at a solution

    I know that the equation they gave us above is the differential equation for ρ*v*A = constant, I just don't know where to go from there.
  2. jcsd
  3. Feb 2, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi tophat22! :smile:

    In steady flow, mass in = mass out of any surface, so ρ*v*A = constant.

    So differentiate ρ*v*A, and divide by ρ*v*A. :wink:
  4. Feb 2, 2009 #3
    I actually ended up getting it before that... thank you though!
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