question_answer

Steam flows at the rate of 10 kg/s through a supersonic nozzle. Throat diameter is 50 mm. Density ratio and velocity ratio with reference to throat and exit are respectively 2.45 and 0.8. What is the diameter at the exit'?

A) 122.5 mm                     

B) 58 mm

C) 70 mm             

D) 62.5 mm

Correct Answer: C

Solution :

\[{{\dot{m}}_{s}}=10\,\text{kg/s,}\] \[{{d}_{1}}=50\,mm\text{,}\] \[\frac{{{\rho }_{1}}}{{{\rho }_{2}}}=2.45,\] \[\frac{{{c}_{1}}}{{{c}_{2}}}=0.8\]             \[{{A}_{1}}{{c}_{1}}{{\rho }_{1}}={{A}_{2}}{{c}_{2}}{{\rho }_{2}}\]             \[{{A}_{2}}=\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{c}_{1}}{{\rho }_{1}}}{{{c}_{2}}{{\rho }_{2}}}=0.8\times 2.45=1.96\]             \[{{d}_{2}}={{d}_{1}}{{d}_{2}}={{d}_{1}}\sqrt{1.96}=50\]             \[50\sqrt{1.96}=70\,\,mm\]