Question

Carbon dioxide enters an adiabatic nozzle steadily at 1 MPa and 500°C with a mass flow rate of 6000 kg/h and leaves at 100 kPa and 450 m/s. The inlet area of the nozzle is 40 cm2 Determine (a) the inlet velocity and (b) the exit temperature.

Answer 1

Step 1 Given let pressure R-1 MPa Inlet temperature T = 500°C Inlet cross sectional area A-40 cm2-0.004 m2 Exit pressure R-100 kPa Exit velocity 450 m/s Mass flow rate of carbon dioxide m = 6000 kg/h 6000 60x60 唐: 1.67 kg/s

Step 2 From the table molar mass, gas constant and critic al point properties The gas constant of Carbon dioxide is R 0.1889 kJ/kg K Molar mass M 44kg/kmol

Step 3 (a) The inlet velocity The mass flow rate is expressed as From ideal gas equation 91 RT 1000 (0.1889) (500+273) A 6.848 kg/m3

Step 4 Therefore the inlet velocity is M2 24 1.67 6.848x0.004 60.96 m/s

Step 5 (b) The exit temperature The energy balance equation per unit mass for a steady state process is Here q--0 andz22 (Since adiabatic and no boundary work) And h-c,T =w= and z-

Step 6 Therefore (12-21 ) From ideal gas specific heats of common gases at c,1.156 kJ/kg K Then 0 = 1.156(7-500)+ 72-500-85. 979 T2=414.021°C 500°C 4502-60.961 011(-500)+450P-60.98 1 (1000) 2687 021K The exit temperature T 687.021K