A turbofan engine is being designed for a bypass ratio of 6:1. During cruise (M=0.85) at 12,000 km, the ratio of the exit stagnation pressure to ambient pressure po/p„ is 1.6:1 (the same for the fan as for the core engine). The stagnation temperature at exit from the core engine is 600 K; at exit from the fan it is only 340 K. The question is whether: a. The fan and core streams should expand in separate nozzles to ambient pressure, or b. They should first be mixed to uniform stagnation temperature, then expanded in a single nozzle. Determine the rats of thrusts (case a to case b) on the understanding that mixing of the two streams can be done with no loss in stagnation pressure. For simplicity, assume that the specific heat ratio and the gas constant are the same for both streams and that y = 1.4 and R = 0.287 The fuel-air ratio for the core engine is approximately 0.018, and nozzle losses are negligible.