Problem $2(25$ points$)$

As mentioned in class, propulsion engineers often determine the efficiency of a rocket based on

measured test data compared to theoretical values predicted by assuming an ideal rocket. For

a liquid rocket engine, propellant flow rates into the chamber are measured using flowmeters

and the thrust is measured using load cells. Internal chamber conditions $($other than pressure$)$

are estimated using thermochemistry and combustion codes. Typical data may look like

below:

Note that $d_t$ and $d_e$ are the nozzle throat and exit diameters, respectively. From this infor$-$

mation, calculate:

$($a$)$ Ideal $c_{id}^{*}$ from calculated propellant conditions

$($b$)$ Ideal $C_{F,id}$ using measured pressures

$($c$)$ Ideal thrust $F_{t,id}$ and mass flow $m_{id}^{}$

$($d$)$ Actual $c^{*}$ delivered during the test

$($e$)$ The "thrust efficiency" ${}_F=\frac{F}{F_{t,id}}$

$($f$)$ The $"c^{*}$ efficiency" ${}_{c^{*}}=\frac{c^{*}}{c_{id}^{*}}$

$($g$)$ Ideal $I_{sp,id}$ and actual $I_{sp}$