$($a$)$ Air flows steadily between two cross sections in a long, straight section of $0\mathrm{.}1-$m$-$inside$-$diameter pipe. The static temperature and pressure at each section are indicated in the figure below. If the average air velocity at section $(1)$ is $205\frac{m}{s},$ determine the average air velocity at section $(2).$ Treat air as ideal gas.

Note: Start with Eq$.4\mathrm{.}19,$ then apply the necessary assumptions and approximations to obtain the equation required to solve the problem. Sketch the control volume.

$p_1=77$kPa$(\frac{?}{abs})$

$T_1=268K$

$V_1=205\frac{m}{s}$

$p_2=45$kPa $(abs)$

$T_2=240K$