$1.(10$ pts$.)$Consider two versions of a jet engine.The first is a standard engine run with a turbineinlet temperature ofT$=1200$ K$.$The second engine is identical, except that its turbine ist$4$cooled by bleeding air from the compressor, which allows the turbine inlet temperature to beraised toT$=1600$ K$.$The basic engine and the bleed$-$air line are as sketched.To estimatet$4$the effect of the cooling$-$air modification on the engine performance, take the engine to beflying at Mach $2$ at an altitude where the ambient temperature isT$=200$ K$,$ and take the$0$compressor pressure ratio to be$=9.$In the modified engine, $10\%$ of the compressorcdischarge air $($at stagnation temperatureT$)$ is diverted for turbine cooling.That air is thent$3$discharged with negligible velocity.Assume all components of both engines are ideal, andtake$=1\mathrm{.}4$ andc$=1\mathrm{.}0$ kJ$/$kg$-$K$.$p Consider two versions of a jet engine. The first is a standard engine run with

a turbine inlet temperature of $1200$ K $.$ The second is identical, except that its

turbine is cooled by bleeding air from the compressor; in this way the allow$-$

able turbine inlet temperature may be raised to $1600$ K $.$ The basic engine and

the bleed air line are indicated in the figure. To make an estimate of the ef$-$

fect of this modification on the thrust, suppose that the engine is flying at

Mach $2$ at an altitude where the ambient temperature is $200$ K and that com$-$

pressor pressure ratio is $9$:$1.$ Suppose also that for the second engine $10\%$ of

PROBLEM $9$ the airflow is bled from the compressor at a point where the pressure ratio is

$9$:$1.$ After cooling the turbine, the bleed air is exhausted from the engine

with no appreciable velocity. For simplicity assume all components of both

engines to be reversible. Let $=1\mathrm{.}4$ and $c_p=1\mathrm{.}0k\frac{J}{kg*K}.$

a$.$ Determine the thrust of the two engines per unit mass flow of air enter$-$

ing the compressor.

b$.$ What is the ratio of the thrust specific fuel consumption of the second

engine to that of the first?