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Equation manipulation, fluids

  1. Jan 25, 2010 #1
    I am not entirely sure how some of these steps work.

    What I have so far (pardon any latex mistakes, I am new to it)

    Code (Text):
    K=\frac{\Delta P}{\Lambda Vol /Vol}
    change in pressure over volumetric strain = K the bulk modulus

    Code (Text):
    \rho Vol'= d \rho / dt
    Code (Text):
    (\frac{d P}{d t}/\frac{d \rho}{d t}*)\rho=K
    I am unsure about this step del P to dP/dt i understand but not the strain term.


    Code (Text):
    \frac{d P}{d t}= \frac{K}{p} * \frac{\rho}{dt} = K Vol'

    Code (Text):
    Vol'=div(V)
    V is velocity

    Code (Text):
    \frac{d P}{d t} = K div (V)
    because
    Code (Text):
    \frac{d P}{d t} =div(M*grad(P))
    Code (Text):
    div(M*grad(P))= K div (V)
    These last two steps I don't understand apparently \frac{d P}{d t} =div(M*grad(P)) is some kind of identity. And because I don't understand this step I don't understand what value M should have.

    Any light on these would be awesome thanks. Sorry its kinda messy im very new to latex
     
  2. jcsd
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