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 cin=10 m/s under the pressure pin=1bar and the temperature ϑin=25°C. At the outlet side air flows out of the pipe with velocity cout=150 m/s under the pressure pin=0.8bar.
1) Determine whether this pipe is nozzle or diffuser without calculating the ratio of cross section of outlet and inlet Aout/Ain
2) Determine now the ratio of cross section of outlet and inlet Aout/Ain
Air can be considered as perfect gas with cp=1 J/K∙g and R=0.29 J/K∙g
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 hin=cp·Tin und hout=cp·Tout
Therefore the temperature of air at the outlet side is:
We now calculate the entropy change during this process:
Hence it is Nozzle.
In order to determine Aout/Ain, we need additional the law of conservation of mass and the ideal gas law:
Ain>Aout , it is also proved that this pipe is a nozzle.