Question 6.13: Problem: Argon enters an adiabatic nozzle at 4 bar and 850 °...
Problem: Argon enters an adiabatic nozzle at 4 bar and 850 °C and exits at 1 bar. If the isentropic efficiency of the nozzle is 90%, find the exit velocity and temperature of the gas.
Find: Exit velocity \pmb{V} _2 and temperature T_2 of argon.
Known: Inlet temperature T_1 = 850 °C = 1123.15 K, inlet pressure P_1 = 4 bar, exit pressure P_2 = 1 bar, isentropic efficiency η_n = 0.9.
Assumptions: Argon is an ideal gas with constant specific heats.
Governing Equations:
Isentropic nozzle efficiency \eta _{\text{nozzle}}=\frac{\pmb{V}_2^2}{\pmb{V}_{2s}^2}
Nozzle exit velocity \pmb{V}_2=\sqrt{2(h_2 – h_1)} =\sqrt{2c_p(T_2 – T_1)}
Isentropic process (ideal gas, \frac{T_2}{T_1} =\left\lgroup\frac{P_2}{P_1} \right\rgroup ^{(\gamma -1)/\gamma }
constant specific heats)
Properties: Argon at 25 °C (approximation) has specific heat c_p = 0.520 kJ / kgK (Appendix 1), specific heat ratio of argon at 25 °C (approximation) \gamma = 1.667 (Appendix 1).
