Question

Problem 2 was...

3. For the nozzle of problem 2, what pressure would a pitot tube read if inserted where A/At 1.14 (a) in the subsonic section; (b) in the supersonic section?; (c) what increased nozzle exit pressure would cause a shock to occur at A/At 1.25? (d) what would be the pitot tube pressure reading just upstream and just downstream of this shock? Approx. Ans: (a) Po 1.7 MPa; (b) Po 1.2 MPa; (c) Pe0.7 MPa; (d) Po 0.97 MPa At

Air exapands in a frictionless adiabatic flow through a converging-diverging nozzle at a mass flow rate of 2.5 kg/s. Source stagnation condition are 1.1 Mpa and 115 C. If the nozzle exit pressure is 141 kPa, and there are no shocks in the nozzle, find the (a) the exit area Ae; (b) the throat At.

And I got (a) Ae = 1.11 * 10^(-3) m^2 and (b) At = 1.87 * 10^(-3) m^2

Answer 1

The flow situation being considered is shown in the figure below. We know that p_0/p = [1 + gamma-1/2 Ma^2]^gamma/gamma-1 Mach number at the exit is Ma_1 = [2/gamma-1{(p_0/p_1)^gamma-1/gamma-1}]^1/2 = [2/1.4-1{(1.1/0.141)^1.4-1/1.4-1}]^1/2 = 2.0 We know that T_0/T_1 = 1 + gamma-1/2 Ma^2_1 Temperature of air at the exit is \r\n T_1 = T_0/1 + gamma-1/2 Ma^2_1 = 388/1 + 1.4-1/2 (2)^2 = 216K Velocity of air at exit is found to be V_1 = Ma_1C_1 = Ma_1(gamma RT_1)^1/2 = 2.0 times (1.4 times 287 times 216)^1/2 = 589 m/s The density of air at exit is given by p_1 = p_1/RT_1 = 141 times 10^3/287 times 216 = 2.27 kg/m^3 Since ma_1 = 2.0, nozzle must be chocked and Ma_1 = 1.0. Pressure at throat is P_r = P_0/[1 + gamma-1/2 Ma^2_r]^gamma/gamma-1 = 1.1 times 10^6/[1 + 1.4-1/2 (1)^2]^3.5 = 581 kPa Temperature at throat is t_t = T-0/1 + gamma-1/2 Ma^2_1 = 388/1 + 1.4-1/2 (1)^2 = 323K The density of air at throat is given by