Question

Consider a turbojet powered airplane flying at a standard altitude of 30,000ft at a velocity of 500 mph. The turbojet engine itself has inlet and exit areas of 7 ft 2 and 4.5 ft2, respectively. The velocity and pressure of the exhaust gas at the exit are 1600 ft/s and 640 lb/ft2, respectively. Calculate the thrust of the turbojet. (Use the TSA value of pressure and density at the altitude of 30,000ft)

Answer 1

Answer:

T  = 20.42 N

Explanation:

given data

standard altitude = 30,000 ft

velocity Ca = 500 mph = 0.4 m/s

inlet areas Aa = 7 ft² = 0.65 m²

exit areas Aj = 4.5 ft²  =  0.42 m²

velocity at exit Cj = 1600 ft/s = 487.68 m/s

pressure exit $\rho$j = 640 lb/ft²   = 0.3 bar

solution

we get here thrust of the turbojet that is  express as

thrust of the turbojet T = Mg × Cj - Ma × Ca + ( $\rho$j Aj - $\rho$a Ag )   .............1

here Ma = Mg

Ma = $\rho$a × Ca Aa = 0.042 kg/s

put value in equation 1 we get

T = 0.042 × (487.68 -0.14) + ( 0.3 ×  - 0.3 × 0.65 )  

T  = 20.42 N

Answer 2

The required thurst is 4010.2539 lb.

Given,

$V\infty =500mph=733.333 \ ft/s$

$A_{i}=7 \ ft^{2$

$A_{e}=4.5 \ ft^{2}$

$P_{e}=640 \ lb/ft^{2}$

$V_{e}=1600 \ ft/s$

Assuming mass flow rate is the same at inlrt of exist.

$m_{i}=m_{e}=m=S_{\infty }V_{\infty }A_{i}$

At $30000ft$, Air properties table.

$S_{\infty }=8.91\times 10^{-4} \ slugs/ft^{3}$

$P_{\infty }=4.373 \ lb/m^{2}=629.712 \ lb/ft^{2}$

$m^{\circ}=8.91\times 10^{-4}\times 733.33\times 7=4.57378 \ slugs/s$

The thrust of a turbojet is given by

$T=m\left ( V_{e}-V_{\infty } \right )+\left ( P_{e} -P_{\infty }\right )A_{e}$

$T=4.57378\left ( 1600-733.33 \right )+\left ( 640- 629.712\right )\left ( 4.5 \right )$

$T=4010.2539 \ lb$

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