# Equation manipulation, fluids

1. Jan 25, 2010

### Halitus

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):
Code (Text):
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