Space Exploration Technologies Corporation (SpaceX) has been making a lot of headlines lately with some impressive feats of technology. Elon Musk and his crew are trying to bring the cost of spaceflight down and so they have decided to return their first stage rockets back to the launch site ready for another flight. Check this out from a few days ago: https://youtu.be/_ETyyEwwTUK. Impressive! This would not be possible without the help of fluid mechanics and heat transfer. Consider the test rig at a SpaceX test facility with the Merlin Engine attached to what must be a very heavily reinforced ceiling shown in Figure 3. There is an oxidant and fuel mixture being injected at the top of the engine. The oxidant has a density of 1141 kg/m and enters the combustion chamber through a 0.7 m hole with a uniform velocity of Vox = 0.5 ms-. The fuel enters with a mass flow rate of mf = 50 kg s-. The exiting gas can be assumed ideal with a molar mass of 22 kJ/kmol and pressure equal to atmospheric pressure. The exhaust has a velocity profile given by Vout (r) = a(r = r), with a = 6000 m-s and an exhaust radius of ro = 0.6 m, using the coordinate system shown in Figure 3. Questions: (a) What is the temperature of the output gas? (b) What is the reaction force R where the rocket meets the ceiling as shown in the free body diagram in Figure 3? Have a look at the SpaceX website where they describe the Falcon 9 rocket: http://www.spacex.com/falcon9. Is this reaction force plausible? Vox me *Vout (r) Figure 3: The Merlin engine from SpaceX at a testing facility (left) and a free body diagram of the engine (right).