Question

Carbon dioxide enters an adiabatic nozzle steadily at 1 MPa, 518 oC, and mass flow rate of 5,322 kg/h and exits the system at 96 kPa and 421 m/s. Considering the nozzle having an inlet area of 37 cm2, calculate the inlet velocity in m/s

Answer 1

Answer:

The velocity at the nozzle at inlet $V_{1}$ = 3584 $\frac{m}{sec}$

Explanation:

Pressure at inlet $P_{1}$ = 1 × $10^{6}$ Pa

Temperature at inlet $T_{1}$ = 518 ° c = 791 K

Mass flow rate = $\frac{5322}{60}$ $\frac{kg}{sec}$ = 88.7

Gas constant for carbon die oxide is R = 189 $\frac{J}{kg k}$

Mass flow rate inside the nozzle is given by the formula = $\frac{P_{1} }{R T_{1} }$ × $A_{1}$ × $V_{1}$

⇒ $P_{1}$ = = 1 × $10^{6}$ Pa

⇒ R$T_{1}$ = 791 × 189 = 149499 $\frac{J}{kg}$

⇒ $A_{1}$ = 0.0037 $m^{2}$

Put all the above values in above formula we get,

⇒ 88.7 = $\frac{10^{6} }{149499}$ × 0.0037 × $V_{1}$

⇒ $V_{1}$ = 3584 $\frac{m}{sec}$

This is the velocity at the nozzle at inlet.