question is given in the image below: The thrust of a turbojet for supersonic sp

Question

question is given in the image below:

The thrust of a turbojet for supersonic speeds is given by T/TM-1 = [1+1.18(M infinity -1 -0.25M infinity 2], for 1 M infinity 3 Assume that TM-1 = 4000 lb and that the thrusts specific fuel consumption (TSFC) is not constant for 1 M infinity 3 but is obtained from TSFC = 1.0 - (T /M-1)* M infinity /10. Find the maximum thrust Find the Mach number where the TSFC is minimized and the thrust of the turbojet for (TSFC)min Plot TSFC and thrust for 1 M infinity 3

Explanation / Answer

1). T= 40000[1+1.18(M-1)-0.25M^2]

for maximum thrust dT/dM=0

0r 1.18-0.5M=0

ot M=2.36

so thrust maximum= 4000[1+1.18*(2.36-1)-0.25*(2.36)^2]

=4849.6 lb

b).now TSFC= 1- [1+1.18(M-1)-0.25M^2]*10/root M

so it is minimum wheh its derivative is =0

so M( 1.18-0.5M)-[1+1.18(M-1)-0.25M^2 =0

or

2.36M-M^2+0.25M^2+0.18-1.18M=0

or M=1.71

thus march number is 1.71

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