An end$-$burning composite solid rocket motor is designed to produce an optimal

thrust of $5$ kN at an altitude of $5$ km where the ambient pressure is $54$ kPa $.$ The

propellant properties are given in Table Q$3.$

a$)$ Draw a process diagram for this engine showing your stage

notation.

b$)$ Assuming an ideal rocket, determine:

$($i$)$ the nozzle exit velocity;

$($ii$)$ the nozzle exit diameter;

$($iii$)$ the throat velocity;

$($iv$)$ the propellant grain diameter;

$($v$)$ the burning time if the propellant charge length is $1\mathrm{.}4$ m ;

$($vi$)$ the thrust if the altitude of the rocket increases to $7$ km

where the ambient pressure is $41$ kPa $.$

Table Q$3$: Rocket engine performance data