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

The velocity at the nozzle at inlet
`V_(1)` = 3584
`(m)/(sec)`

Step-by-step explanation:

Pressure at inlet
`P_(1)` = 1 ×
`10^(6)` Pa

Temperature at inlet
`T_(1)` = 518 ° c = 791 K

Mass flow rate =
`(5322)/(60)`
`(kg)/(sec)` = 88.7

Gas constant for carbon die oxide is R = 189
`(J)/(kg k)`

Mass flow rate inside the nozzle is given by the formula =
`(P_(1) )/(R T_(1) )` ×
`A_(1)` ×
`V_(1)`

⇒
`P_(1)` = = 1 ×
`10^(6)` Pa

⇒ R
`T_(1)` = 791 × 189 = 149499
`(J)/(kg)`

⇒
`A_(1)` = 0.0037
`m^(2)`

Put all the above values in above formula we get,

⇒ 88.7 =
`(10^(6) )/(149499)` × 0.0037 ×
`V_(1)`

⇒
`V_(1)` = 3584
`(m)/(sec)`

This is the velocity at the nozzle at inlet.