At some section in the convergent-divergent nozzle, in which air is flowing, pressure, velocity, temperature and cross-sectional area are $200 \mathrm{kN} / \mathrm{m}^{2}, 170 \mathrm{~m} / \mathrm{s}, 200^{\circ} \mathrm{C}$ and $1000 \mathrm{~mm}^{2}$ respectively. If the flow conditions are isentropic, determine :

(i) Stagnation temperature and stagnation pressure,

(ii) Sonic velocity and Mach number at this section,

(iii) Velocity, Mach number and flow area at outlet section where pressure is $110 \mathrm{kN} / \mathrm{m}^{2}$,

(iv) Pressure, temperature, velocity and flow area at throat of the nozzle.

Take for air $: R=287 \mathrm{~J} / \mathrm{kg} K, c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} K$ and $\gamma=1.4$.

Solution:

Let subscripts 1, 2 and t refers to the conditions at given section, outlet section and throat section of the nozzle respectively.

Pressure in the nozzle, $ \quad p_{1}=200 \mathrm{kN} / \mathrm{m}^{2} \\ $

Velocity of air, $ \quad V_{1}=170 \mathrm{~m} / \mathrm{s} \\ $

Temperature, $ \quad T_{1}=200+273=473 …