Question

Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is $80c{m}^2$. The specific heat of air $c_p$ is 1008 J/kgK

The exit area of nozzle in $c{m}^2$ is

• A. 90.1
• B. 56.3
• C. 4.4
• D. 12.9

Answer 1

The correct option is D 12.9

(d)
Continuity equation for compressible flow
$\rho A_1{V}_1={\rho }_2{A}_2{V}_2$
and, $\frac{A_1{V}_1}{v_1}=\frac{A_2{V}_2}{v_2}$

$\frac{A_1{V}_1}{\frac{R{T}_1}{p_1}}=\frac{A_1{V}_1}{\frac{R{T}_1}{p_1}}$ $(\because pv=RT)$

$\frac{A_1{V}_1{p}_1}{T_1}=\frac{A_2{V}_2{p}_2}{T_2}$

$\frac{80\times 10\times 300}{500}=\frac{A_2\times 180\times 100}{484}$

$A_2=12.90c{m}^2$