For the aircraft with two-shaft engines cruising at 31000ft (Ta = 226.73K, P = 28700 Pa), the first rotor of the core compressor is shown in Figure 1 below. The flow coefficient (axial velocity/ blade speed) Vx / Ut at blade tip is 0.5 with a gas angle for absolute velocity of 3 degrees and the relative Mach number at the tip of the first rotor of core compressor is to be 1.1. Taking the static temperature T23 into the core compressor to be 250K, and the pressure ratio of the compressor is 25. Ut V Figure 1. a) Calculate the rotor blade tip speed Ut. b) The enthalpy rise in each compressor stage is to be equal and is not to exceed 0.42U, where Um is the mean blade speed and the ratio of mean radius and tip radius is 0.75, and the efficiency of the whole compressor is estimated to be 90%. If the stagnation temperature into the core compressor is T023 = 265K, calculate the number of stages in the core compressor and the average value of Aho/U per stage. c) When cruising at 33000ft (T = 222.82K, Pa = 26000 Pa) with a Mach number of 0.75, each aircraft engine has a mass flow rate of 530kg/s and a net thrust of 67000N. The total cross section area of nozzle is 3.6m and the front fan diameter is 2.2m. If at sea level, where the atmospheric pressure and temperature are 101300Pa and 288K respectively and when flying at a Mach number of 0.3, the engine has the same temperature ratio T04/ To2 at 33000ft, calculate the gross thrust at the sea level.