# 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 $2.8$

• Meanwhile does someone explain me better which are the coordinate taken and why does the book use, in this case, the speed of sound (that is speed of disturbance) is taking the part of flow particle speed even using it inside the Equations of mass continuity and Eulero motion? Mar 16 '17 at 17:51
• You should probably accept the answer if it fits your original question and open a new one for your other query. Mar 16 '17 at 20:09
• Yes, AEhere, I opened a new question, that is possible to find at the following link: engineering.stackexchange.com/questions/14326/… If you know someone who can help me and answer the question I will be very grateful. Mar 20 '17 at 14:31