Question

Argon gas enters a converging-diverging nozzle at 60 m/s, 310 °C, and 300 kPa, and it leaves the nozzle at a supersonic velocity. The throat diameter is 3 cm. For Argon R= 208.1 Pa.m3/kg.K; k= 1.667. Determine (a) the stagnation temperature and pressure (8 points) (b) the critical temperature and pressure at the throat (7 points) (c) the velocity at the throat (4 points) (d) the mass flow rate. (6 points)

Answer 1

Solution Given Porto d* - 3 cm ן ויין (Stagnation properties) | k=1:667 R = 20801 Pa throat Pa miling Exit Inlet y = 60ml sec T= 310°c - 583k P = homsee Book Pa •) Stagnation temperature (To) and Pressure (P) – Given- V = 60 m/sec = M, JK RT, to = M, S10667 X208.1X583 60 = M, (449,715) M 0.1334 Relation blw stagnation tempera Fure and statie temperature at any point To (1+ k,, mp) TE it KIM? то 583 It 1.667-1 10.1334)? 2 To=586.46k Also, Vel 1.667 + 0.667 300 (+ 1-667-1.60.1334) Pi 2 P = 304.5 kPa

Critical temperature (7*) and critical pressu essure (p*) at throat - T* -To = 586.46 ( 22.667 kt T* = 439.79k 1.667 0.667 p* = Po 2 kt - 304.5 (22062 2.667 p* = 148:32kPa 9 Velocity at throat - at throat, mach number 1 so V* KRT * = 51667) (20801) (439079) V*= 390.6 m/sec | d) Mass flow rate is & AV = constant given by - * V * S, AV so, m S А * Α* V p* RT* 148.32 x loud x 30 14 x (31² x 10-4 x 390.6 208.1x439.79 = 0.447 kglser kalsee