Problem $1$

Consider an ideal air$-$standard cycle for a gas$-$turbine jet propulsion unit. The pressure and

temperature entering the compressor are $90$ kPa and $290$ K$,$ respectively. The pressure ratio

across the compressor is $14$:$1.$ The turbine inlet temperature is $1500$ K$.$ When the air leaves the

turbine, it enters the nozzle and expands to $90$ kPa. Show the process on a T$-$s diagram with

clearly labeled points.

Calculate:

$($a$)$ The velocity of the air leaving the nozzle

$($b$)$ Repeat $($a$)$ for pressure ratio across the compressor of $10$:$1$

$($c$)$ Repeat $($a$)$ for pressure ratio across the compressor of $20$:$1$

$($d$)$ Make a plot of compressor pressure ratio $($abscissa$)$ vs enthalpy change across the nozzle

$($ordinate$)$ for compressor ratios from $10$:$1$ to $26$:$1($in increments of $2)$

$($e$)$ Discuss briefly what happens to the enthalpy change across the nozzle for the compressor

pressure ratios in $($d$)$

$($f$)$ Make a plot of compressor pressure ratio $($abscissa$)$ vs velocity leaving the nozzle

$($ordinate$)$ for compressor ratios from $10$:$1$ to $26$:$1($in increments of $2)$

$($g$)$ Discuss briefly what happens to the velocity leaving the nozzle for the compressor

pressure ratios in $($f$)$