Question

SP 7. The SpaceX Super Draco reaction control thrusters employ a converging-diverging nozzle to isentropically accelerate the flow of combusted monomethyl hydrazine/nitrogen tetroxide gases to supersonic speeds. The throat area in these engines is At = 0.0345 m2 https://internetprotocol.co/content/images/2020/01/Space-X.png a) Given that the pressure and temperature within the combustion chamber (where velocity 0) are po = 5 MPa and To = 3600 K, respectively, and that the flow exits the nozzle at an exit pressure, Pe 0.5 MPa , find the Mach number at the exit of the rocket engine. The ratio of specific heats for the combusted gases is y = 1.2. b) We will learn that rocket thrust is maximized when the exit pressure is equal to the surrounding ambient pressure, or pe = Pa. For the configuration in part a), find the exit area, Ae

Answer 1

In the question ambient pressure is not given so I am assuming it to be 100KPa.

a) Given to page No 0 Po=SMPa f To = 36ook Pe=o =05 MPa Monomethyl hydrazine (molecular weight = 4607g/mol) VIR 12 gas > op ) ®314.47 46.07 NAIM 1.2-1 ligk (p = JOB.2.70 J for isentropic process 3 fi (Т. 12-1 1.2 il 0.5 5 Te I (Pe To Po Tes 2452.65 k Exit Velocity = 12 cp (Jo-tel **** (ve) 2x 1087.78 (3600 -2458.65) IVe- 1576-277 ml sector Mach Number m= Ve ve 1576 277 343 Arsons M = 4.5 CS Scanned with CamScanner

Page Nog Pa TH TQ (lo 100 Sooo b) if pe = Pa combient pressure) Let Pa = 100 kPa Cass assuming Te To Po Te=1875.6k Ve = $200 (To-Te) JQX 1082.78 (3600 - 1875.6) Ve= 1992.43 m/see m= PO AM ra ✓ To R 5xlo@x0-0345 12 3600 (6314/46.07) 1.2+1 m = 138.79 Kgls rt het) rti 9 1-9 + 1-2-1 m=seve te Se- Pe R Te 100 8314 46.07 Je = 0.295 kg/m3 138-79= m = 0.295x1932.43X Ae Tae = 0·843m2 Ansur CS Scanned with CamScanner