Air enters the diffuser of a ramjet engine $($schematic shown below$)$ at $6lb\frac{f}{i}{n}^2,420R,$ with a velocity of $1800f\frac{t}{s},$ and decelerates essentially to zero velocity. After combustion, the gases reach a temperature of $2000R$ before being discharged through the nozzle at $6lb\frac{f}{i}n.{?}^2$

On the basis of an air$-$standard analysis, determine:

$($a$)$ the pressure at the diffuser exit, in Ibf$/$in$.{?}^2$

$($b$)$ the velocity at the nozzle exit, in $f\frac{t}{s}.$

Neglect kinetic energy except at the diffuser inlet and the nozzle exit. Assume combustion occurs at constant pressure and flow through the diffuser and nozzle is isentropic$.$

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