# Roskam book uses Eulero motion eq. and mass continuity eq. to find speed of sound but (in my opinion) not in a coherent use (about density variation)

As you can see inside this following link:  https://books.google.it/books?id=bSq-cEf0EWsC&pg=PA19&lpg=PA19&dq=Aerodynamic+2.3.2+The+speed+of+sound&source=bl&ots=iFRByWKpwG&sig=MpcRIKUA6tsAwsEzG5lwOnRuySQ&hl=it&sa=X&ved=0ahUKEwjfjb_o0dXSAhWLOxQKHRjIB40Q6AEIITAA#v=onepage&q=Aerodynamic%202.3.2%20The%20speed%20of%20sound&f=false  Jan Roskam's book : Airplane Aerodynamics and Performance, Chapter 2 Basic Aerodynamic Principles and Application, Subparagraph 2.3.2 THE SPEED OF SOUND, uses continuity equation: (2.2) $dm/dt= ρAV= cost$ , and, differentianting it for constant area it yields $V_ad ρ+ ρd V_a=0$ (2.28).

Furthermore the book uses The Euler equation of motion, Eq (2.9) $p+{1/2}ρ{V^2}=cost$ in order to yielding $dp+ρV_adV_a=0$. (2.29) In the continuation it eliminates $dV_a$ from Equations (2.28) and (2.29) But equation (2.9) is the form of equation in incompressibiity hypothesis. Why does that book use mass continuity equation in condition of density not changing (incompressibility) (i.e. disregadind density variation term) in conjunction of another equation where it uses compressibility variation? furtheremore compressibility variation (in form of derivative) is used in the yielded equation (2.30) too: ${V_a}^2=dp/dρ$

It's a typo and he's actually changing the form of Eq. $2.8$, thus not applying the $\rho = constant$ constraint. So he says he's rewriting $2.9$, but actually rewrites $2.8$