Question

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging diverging nozzle of exit area $0.005m^2$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively

The density of air in $kg/m^3$ at the nozzle exit is

• A. 0.560
• B. 0.600
• C. 0.727
• D. 0.800

Answer 1

The correct option is C 0.727

(c)
Density of air in $\left(kg/m^3\right)$ at nozzle exit is
$\frac{p_1}{{\rho }_1^{\gamma }}=\frac{p_2}{{\rho }_2^{\gamma }}$
where $\rho =Density$
${\rho }_2=(\frac{p_2}{{\rho }_1}{)}^{\frac{1}{\gamma }}$${\rho }_1$
Also,
$\because$ $p_1{V}_1=mR{T}_1$
$\frac{p_1}{R{T}_1}=\frac{m}{V_1};$ ${\rho }_1=\frac{p_1}{R{T}_1}$
$\therefore$ $={\rho }_2(\frac{50}{300}{)}^{1/1.4}\times \frac{3\times {10}^5}{0.287\times 1000\times 400}$
$=0.727kg/m^3$