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.