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Engineering and Tech / Fundamentals of Thermodynamcs 8 / Chapter 4 / Problem 30HP

Fundamentals of Thermodynamcs | 8th Edition | ISBN: 9781118131992 | Authors: Claus Borgnakke, Richard E. Sonntag

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Nozzles, DiffusersThe front of a jet engine acts similarly

Chapter 4, Problem 30HP

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QUESTION:

Problem 30HP

Nozzles, Diffusers

The front of a jet engine acts similarly to a diffuser, receiving air at 900 km/h, −5°C, and 50 kPa, bringing it to 80 m/s relative to the engine before entering the compressor (see Fig. P4.30). If the flow area is increased to 120% of the inlet area, find the temperature and pressure in the compressor inlet.

FIGURE P4.30

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QUESTION:

Problem 30HP

Nozzles, Diffusers

The front of a jet engine acts similarly to a diffuser, receiving air at 900 km/h, −5°C, and 50 kPa, bringing it to 80 m/s relative to the engine before entering the compressor (see Fig. P4.30). If the flow area is increased to 120% of the inlet area, find the temperature and pressure in the compressor inlet.

FIGURE P4.30

ANSWER:

Solution 30 HP:

Step 1 of 3:-

Here we have to find the temperature and the pressure in the compressor inlet.

The rate of receiving air is 900 km/hr.

The temperature and pressure of the receiving air are $-{5}^{0}\ C$ and 50 kPa.

The flow area is increased by 120% of the inlet area.

The continuity equation tells that,

$\dot{{m}_{i}}=\dot{{m}_{e}}$

But this must be equal to $AV/v$ .

The energy equation will be,

$\dot{m}\left({{h}_{i}+\frac{1}{2}{{V}_{i}}^{2}}\right)=\dot{m}\left({\frac{1}{2}{{V}_{e}}^{2}+{h}_{e}}\right)$

$\Rightarrow{}{h}_{e}-{h}_{i}={C}_{P}\left({{T}_{e}-{T}_{i}}\right)$

$=\frac{1}{2}\left({{{V}_{i}}^{2}-{{V}_{e}}^{2}}\right)$

$=\frac{1}{2}\times{}[{\left({\frac{900\times{}1000}{3600}}\right)}^{2}-8{0}^{2}]$

$=28050\ J/kg$

$=28.05\ KJ/kg$ .

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