We discussed in class that the situation of a choked flow with a normal shock inside the nozzle is

likely not optimal for producing thrust. Here, we will examine why. Consider a

converging$-$diverging nozzle with an exit to throat area ratio, $($A$\_($e$))/($A$\_($t$))=6,$ that produces thrust by

steady$-$state quasi$-1$D expansion of calorically perfect Air with a reservoir pressure, P$\_(0)=120$kPa,

and reservoir temperature, T$\_(0)=800$K$.$ Determine:

$($a$)$ Compute mass flow rate per unit exit area, $($m$^())/($A$\_($e$))(($kg$)/($m$^(2))-$s$),$ assuming choked flow for this

nozzle.

$($b$)$ Determine the normalized area position, $($A$\_($thock $))/($A$^(*)),$ of the normal shock for a case where back

pressure, P$\_($back$)=60$kPa. Please use the Matlab Script that has been provided to help you do this.

$($c$)$ Compute the ratio of thrust to exit area, $($F$\_($T$))/($A$\_($e$))($k$($N$)/($m$^(2))),$ for the above case with, P$\_($back $)=60$kPa,

using the same formula that we utilized in problem #$3,$ e$.$g$.$:

$($F$\_(\backslash$tau $))/($A$\_($e$))=((($m$^()))/($A$\_($e$)))$U$\_($e$)+$P$\_($e$)-$P$\_($back$)$

$($d$)$ Compute the ratio of thrust to exit area, $($F$\_($T$))/($A$\_($e$))($k$($N$)/($m$^(2))),$ for the supersonic isentropic$-$root case

where the back pressure is equal to the pressure of ideal supersonic expansion of the nozzle.

SHOW ALL WORK. DO NOT COPY ANYONE ELSES PROBLEMS LIKE THIS, THOSE ANSWERS ARE WRONG, SHOW ALL WORK, ONLY ONLY DO part $($a$)$

HINT:You can start solving this problem by Ae$/$At $=$Ae$/$A$*.$