Question

Air at P₁=3 bar, T₁=288k, M₁=1.5 is brought to sonic velocity in a frictionless constant area duct thought which heat transfer can occur:

1. Determine the final pressure and temperature and the heat add during the process

2. What will be the Mach number, pressure and temperature of air if this heat is extracted from the air?

Answer 1

Where P_1 = 3 bar T_1 = 288 k, M_1 = 1.5 sonic velocity in a frictionless constant area. Given pi_1 = 288 k P_1 = 3 bar M_1 = 1.5 M_2 = 1 1) we know that T_2/T_1 = m^2_2/m^2_1 times (1 + y m^2_1)^2/(1 + y m^2_2)^2 for air put y = 1.4 T_2/T_1 = (1/1.5)^2 times [1 + 1.4 times 1.5^2/1 + 1.4 times 1^2]^2 T_2/T_1 = 1.3288 Now T_2 = T_1 times 1.3288 = 288 times 1.3288 T_2_ = 382.72 k 2) we know that P_2/P_1 = 1 + y m^2_1/1 + y m^2_2 Therefore P_2/P_1 = 1 + 1.4 times 1.5^2/1 + 1.4 times 1 = 1.729 Therefore P_2 = 13 times 1.729 = 5.1875 bar \r\n for ray light's table C_p = 0.444 Here heat transfer's a = C_p Delta T = 0.444 times (38.275 - 288) a = 42.06 k J/kg If heat