The internal loadings a cross section through the 6in diameter drive shaft of a turbine consist of an axial force 2500lb, a bending moment of 1500lb. ft. determine the principal stresses at point b. also calculate the maximum in-plane shear stress at this point.

Air (c-1.006 kj/kg.k, r-0.287 kj/kg.k) enters a nozzle steadily at 280 kpa and 77°c with a velocity of 50 m/s and exits at 85 kpa and 320 m/s. the heat losses from the nozzle to the surrounding medium at 20°c are estimated to be 3.2 kj/kg. determine (a) the exit temperature and (b) the total entropy change for this process. solve this problem using constant specific heats.