Question

Air flows through a converging-diverging nozzle/diffuser. Assuming isentropic flow, air as an ideal gas, and constant specific heats determine the state at several locations in the system. Solve using equations rather than with the tables. Note: The specific heat ratio and gas constant for air are given as k=1.4 and R=0.287 kJ/kg-K respectively. --Given Values-- Inlet Temperature: T1 (K) = 348 Inlet pressure: P1 (kPa) = 544 Inlet Velocity: V1 (m/s) = 122 Area at nozzle inlet: A1 (cm^2) = 8.81 Throat area: A (cm^2) = 5.05 Area at diffuser exit: A (cm^2) = 7.19 a) Determine the Mach number at the inlet. Your Answer = 326 Correct! Exact Answer=0.3263 +/- 9.4E-04 b) Determine the stagnation temperature (K) at the inlet. Your Answer = 356.396 Correct! Exact Answer=355.41 +/- 1.4E+00 c) Determine the stagnation pressure (kPa) at the inlet. Your Answer = 585.556 Correct! Exact Answer=585.62 +/- 2.4E+00 d) Determine the theoretical throat area (cm^2) for sonic flow (A*). Your Answer = 4.659 Correct! Exact Answer= 4.663 +/- 1.2E-02 . e) Determine the Mach number at the throat. Your Answer = Incorrect. f) Determine the temperature (K) at the throat. Your Answer = g) Determine the velocity (m/s) at the throat. Your Answer = h) Determine the pressure (kPa) at the throat. Your Answer = i) Determine the mass flow rate (kg/s) through the nozzle Your Answer = j) Determine the Mach number at the exit.

Answer 1

Griven Data : In let Pressure i Inlet Velocity - MNT 11:4X0.287 X103 x 348 Inlet temperature, Ti = 348k P = 544 kPa Vi 122 m/s Inlet Area, AL 8.81 cm2 Throat areal A 5.05 cm2 Area at Diffuser exit, A = 7.19 cm2 Nowo, Properties of Air K=1.4 R = 0.287 kJ/kg.K. a) Calculation of Mach No at Inlet (M) V My = where C=Speed of sound given medium. Where C= V KRTL 1104x0:287 X103 x 348 122 Ans.(a) → My = 0.326 in С 2 2 b) Stagnation temperature at Inlet. (7.) Using the con = 14 (k-1) To T 2 = To 1+ (K-1) Ma (1.4-1)x(0.326 Ans. (b) 326) - 348/14 3 [14 2 > To = 355.397 K

1 f> Now using = 0.833 Mach No at the throat, Ma! table at Max Am (e) =1 T* To -) T* = 0.833 X355.397 T* = 296.045 K Ans (f) g> Velocity at the throat v* = KRT* V1:48287x 296.045 V* = 344.892 m/s Ans.(g). Pressure at the throat p* 0.5283 Po p* 20:5283 x 585.557 p*=309.349 Kla Ans.(h) 1) Maus flow rate through nozzle (m) 585. 557 0.287 X355.397 Now for Maal = 0.6339 + $*016339x5.741 fo - f* 3.639 kg/m3 m= f*A*V* = 3.6394 5.05010 9 x 344.892 m = 0.634 KgLS Ans. (6) h) 3 Soe Po た R To = 5.741 g/m D* ht