Carbon dioxide enters a converging-diverging nozzle at 50 m/s, 600°C, and 450 kPa, and it leaves the nozzle at a supersonic velocity. The velocity of carbon dioxide at the throat of the nozzle is
A)50 m/s
B)186 m/s
C)323 m/s
D)431 m/s
E)461 m/s

Question

Quizplus · Accepted Answer

Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen. 
k=1.289
Cp=0.846 "kJ/kg.K"
R=0.1889 "kJ/kg.K"
"Properties at the inlet"
T1=600+273 "K"
P1=450 "kPa"
Vel1=50 "m/s"
To=T1+Vel1^2/(2*Cp*1000)
To/T1=(Po/P1)^((k-1)/k)
"Throat properties"
T_throat=2*To/(k+1)
P_throat=Po*(2/(k+1))^(k/(k-1))
"The velocity at the throat is the velocity of sound,"
V_throat=SQRT(k*R*T_throat*1000)
"Some Wrong Solutions with Common Mistakes:"
W1_Vthroat=SQRT(k*R*T1*1000) "Using T1 for temperature"
W2_Vthroat=SQRT(k*R*T2_throat*1000); T2_throat=2*(T_throat-273)/(k+1) "Using C for temperature"
W3_Vthroat=k*R*T_throat "Using wrong relation"

Carbon Dioxide Enters a Converging-Diverging Nozzle at 50 M/s, 600°C