The pressure$-$density relation for ethanol is approximated by $!$

$!!$

$=$ # $"$

$"!$

$

#

with $=1600,=2,$

$$$ $=1$ atm $=105$ Pa$,$ and $$$ $=800$ kg$/$m$\%.1)$ Estimate the speed of sound $($in the unit of m$/$s$)$ of

ethanol at $=1000$ atm. $2)$ If the volume flow of ethanol in a $0\mathrm{.}2$m$-$diameter circular pipe is $6\mathrm{.}28$

m$3/$s$,$ what type of compressible flow is it$?(20$ points$)$