A converging nozzle is attached to a large compressed air $($R $=286\mathrm{.}55$ J$/($kg K$),$ Problem $12.$ A converging nozzle is attached to a large compressed air $,$

$\{$:$=1\mathrm{.}4,C_p=1005\frac{J}{kgK})$ tank with a pressure of $400$ kPa $.$ The air flows through the nozzle

isentropically into an outer space with a certain back pressure.

$($a$)$ Under what back pressure $($in kPa $)$ will the exit Mach number, $M_e,$ be sonic?

Calculate the nozzle exit Mach number for the following back pressures:

$($b$)100$ kPa ;

$($c$)250$ kPa $.$

For the back pressure of $350$ kPa :

$($d$)$ Calculate pressure $($in kPa $)$ at the cross$-$section with area $A_1$ two times larger than the nozzle

exit area $A_e(A_1=2A_e).$

Also answer the following question:

$($e$)$ Can the exit flow be supersonic? Explain.

$\backslash$gamma $=1\mathrm{.}4,$ Cp $=1005$ J$/($kg K$))$ tank with a pressure of $400$ kPa. The air flows through the nozzle

isentropically into an outer space with a certain back pressure.

$($a$)$ Under what back pressure $($in kPa$)$ will the exit Mach number, Me$,$ be sonic?

Calculate the nozzle exit Mach number for the following back pressures:

$($b$)100$ kPa;

$($c$)250$ kPa.

For the back pressure of $350$ kPa:

$($d$)$ Calculate pressure $($in kPa$)$ at the cross$-$section with area A$1$ two times larger than the nozzle

exit area Ae $($A$1=2$Ae$).$

Also answer the following question:

$($e$)$ Can the exit flow be supersonic? Explain