Hye, this is my first time to ask in this group. I am not familiar with fluid mechanics and currently self-learning for postgraduate study and facing difficulties in deriving both 4.9 and 4.11 as below.
for 4.5, I understand it is PDE, but I do not know how they extract porosity and density and differentiate only pressure.
for 4.8, it is simple to integrate, and I managed to bring dp(pressure) to left-hand side (LHS) and by integrate from $p_0$ to $p$, it will give the value as 4.11. However, I do not know where the $\rho$(density) which is p0 came from. I think by integrating $d\ln(\rho)$ which is density it should give initial value $\ln(\rho)$?
Sorry for my bad knowledge, I am trying to refresh my math skills and I do not have a background in fluid mechanics which is crucial for my postgraduate study.
