Can you help with this problem Thanks Use gamma 14 R 287 J

Can you help with this problem? Thanks!!

Use gamma = 1.4, R = 287 J/kg/K^1 and c_p = 1005 J/kg/K in this question. A two-dimensional compressor cascade operates in air. The inlet metal angle of the blades is 55 degree and the exit metal angle is 37 degree. When the flow is at zero incidence with an inlet Mach number of 0.65, the exit Mach number is 0.44, and the stagnation pressure loss coefficient is given by gamma_p = p_01 - p_02/p_01 - p_1 = 0.038 Determine the exit flow angle and give two reasons why this is greater than the exit metal angle. Find the blade pitch-to-chord ratio needed such that DF = 0.45 when the cascade is at the operating point described in part (a). Assuming that the exit flow angle and loss remain constant, estimate the new value of DF when the incidence of the flow is increased to 5 degree while maintaining an inlet Mach number of 0.65. Use the pitch to chord ratio found in part (b). If the cascade throat width to pitch ratio o/s is 0.6, determine the incidence of the flow onto the blades at which the cascade will choke with an inlet Mach number of 0.65. Assume that there is no loss upstream of the cascade throat.

Solution

tan (exit flow angle) = 1/2 * (tan (inlet metal angle) + tan (outlet metal angle))

= 1/2 * (tan 55 + tan 37)

= 1.08

So,

exit flow angle = 47.20

The low amount of diffusion on the suction surface together with the thin boundary layers imply that the flow exit angle is much closer to the metal angle at the trailing edge than for a compressor cascade blade. For supersonic exit flows, exit metal angles are smaller.