Download the exercise with solution: Nozzle and Diffuser

Air flows through an adiabatic and horizontal placed pipe with changeable cross section. At the inlet side air flows with velocity c_in=10 m/s under the pressure p_in=1bar and the temperature ϑ_in=25°C. At the outlet side air flows out of the pipe with velocity c_out=150 m/s under the pressure p_in=0.8bar.

1)      Determine whether this pipe is nozzle or diffuser without calculating the ratio of cross section of outlet and inlet A_out/A_in

2)      Determine now the ratio of cross section of outlet and inlet A_out/A_in

Air can be considered as perfect gas with c_p=1 J/K∙g and R=0.29 J/K∙g

Solution:

1)

The 1.Law of thermodynamics:Stationary → d/dτ=0

Adiabatic → ΣQ=0

Without input and output (work) → ΣW=0

Horizontal placed → no change in potential energy → Δ(g·z)=0

Then we can obtain the simplified 1.Law: wobei h_in=c_p·T_in und h_out=c_p·T_out

Therefore the temperature of air at the outlet side is:

We now calculate the entropy change during this process:

Hence it is Nozzle.

2)

In order to determine A_out/A_in, we need additional the law of conservation of mass and the ideal gas law:

A_in>A_out , it is also proved that this pipe is a nozzle.