Shock wave

** shock wave

thickness of shock wave is order of 1e-7 m

why governed by Euler Equation? P334

shock wave: a large amplitude compression wave, such as
that produced by an explosion, caused by supersonic motion of a body in a
medium

thickness of shock wave ~ 1e-7m

enthalpy, h = e+pV

entropy, s

the shock wave is a thin region of highly viscous flow.
the flow through the shock is *adiabatic* but *nonisentropic*

energy equation for normal shock wave

\begin{equation}
h_1 + 0.5 u_1^2 = h_2 + 0.5 u_2^2
\end{equation}
(eq.8.10, andersion, 6th)

Ch8, andersion, 6th
*** speed of sound

what is the physical mechanism of the propatation of sound waves?

the physical mechanism of sound propagation in a gas
is based on molecular motion

how can we calculate the speed of sound?

what properties of the gas does it depend on?

fundamental expression for the speed of sound in a gas
\begin{equation}
a= sqrt((frac{\partial p}{\partial \rho})s)

\end{equation}

for a perfect gas, speed of soound(a) is a function of temperature only
 a=f(T)

\begin{equation}
a= sqrt(\gamma RT)
\end{equation}
*** when is a flow compressible?
for subsonic flows:
it is a matter of the degree of accuracy desired whether
we treat \rho as a constant or as a variable

for supersonic flow:
the \rho must be treated as variable

*the rule of thumb:*

M<0.3, imcompressbile

M>0.3, compressbile

*** references

7.6 some aspects of supersonic flow: shock waves
ch8, ch9, anderson, 6th