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. 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) = 338 Inlet pressure: P1 (kPa) = 555 Inlet Velocity: V1 (m/s) = 121 Area at inlet (cm^2) = 9 Mach number at the exit = 1.56 a) Determine the mass flow rate (kg/s) through the nozzle Your Answer = b) Determine the Mach number at the inlet. Your Answer = c) Determine the stagnation temperature (K) at the inlet. Your Answer = d) Determine the stagnation pressure (kPa) at the inlet. Your Answer = e) Determine the temperature (K) at the throat. Your Answer = f) Determine the pressure (kPa) at the throat. Your Answer = 8) Determine the velocity (m/s) at the throat. Your Answer = h) Determine the area (cm^2) at the throat. Your Answer = 1) Determine the temperature (K) at the exit. Your Answer 1) Determine the pressure (kPa) at the exit. Your Answer = k) Determine the velocity (m/s) at the exit. Your Answer =

Answer 1

ywensterbart Answer 1 mags flow note m= SI AIV nino Als inlet area 2 9 cm 9x104m2 3 Sie PA 5 5 5x10 RT 281 x 338 [R = 0.281 kl /kg k 284 +/kg k 11 k. Si 5:12 13 kg/m 3 m 5.72 13 x 9 x10-4 *121 [ Vi=121 m/s 3. 0.623 kg/sec b Mach no MI Mia JOR TI 121 (1.48287*338) Mi 0.3283386

2 © Toi = 9 [stagnation temp Toi: Tit V, 2 2xCp Cpair: 1005 /kg k Toi 338 + (121) (2x1005) Toi 345.284 ok Poi- [Stagnation pressure 7-1 Pol Pix (Tol TI 0.4 (555*103] x [345-084 338 POL 598.0017 kpa temp at throat Tthroat

3 at super gonie exit condition Mach no at threat Monroad Tthroat Tol (2+1) Throat 2 87.73 67 of pressure at throat Pthroat Porroat Pol (1+x) 02/12 3 598.00 17 x 10 103 (12) 3-5 Pohroat 315.913 kpa g) velocity at throat Vonroat = 9 V hroat (1.4x 281x 1998.868) 287.7367 Venrost 240 +2311 340 m/s area at throat Athroat

fr+D ax(4-1) AL 311 2+(2-x Mi? (r+ ) Abiroat Mi 3 a + ColX 0.82836 9 Athroat (6-328386) A throat = 4.79 cm2 j temparature at exet Te = 9 To Te = ( 1+ (9-1) XMC2) Me = 1.56 Te 13 345.284 [1+ + (0.2x1.562 Te : 232.245480k ;) pressure at exat pe = o Po Pe /o-1 (1+Cr -1D X Me 2 ) +-

Pe : 598.00 11x103 [1+602x1.5827 79 Pe = 402.228 kpa k) velocity at exat Ves 2xCp (To - Te ut Ve = (ax1005x (345.284 – 232.04548 Ve 476 662 m/s