Carbon dioxide enters an adiabatic nozzle steadily at 1 MPa and 500 C with a mass flow rate of 6000 kg/hr and leaves at 100 kPa and 450 m/s. The inlet area of the nozzle is 40 cm2. Determine the following: a) the inlet velocity.
b) the exit temperature.

a) The inlet velocity, v₁ = 60.95 m/s

b) The exit temperature,

Explanation:

a) Determine the inlet velocity

The gas considered is

The inlet Area of the nozzle, = 0.004 m²

Gas constant for , R = 0.1889 kJ/kg-K

Input Pressure, P₁ = 1 MPa = 1000 kPa

Output Pressure, P₂ = 100 kPa

Input temperature, T₁ = 500°C = 500 + 273 = 773 K

Mass flow rate,

The relationship between mass flow rate and Inlet velocity is given by:

..............(*)

It is necessary to first get the input density, using the relationship below:

Insert the necessary parameters into equation (*) to determine the inlet velocity:

1.67 = 6.85 * 0.004 * v₁

1.67 = 0.0274 v₁

v₁ = 1.67/0.0274

v₁ = 60.95 m/s

b) The exit temperature

At ,

Exit Velocity, v₂ = 450 m/s

In an adiabatic process, there is no exchange of heat

i.e energy expended = work done = 0, q = w = 0

There is no change in potential energy

For a steady state process:

Considering all the assumptions for an an adiabatic process, the equation above reduces to:

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explanation: