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A 3-stage air compressor compresses air from 100 kPa to 700 kPa. Find the intercooler pressure between the 2nd and 3rd stage.

A. 365.88 kPa
B. 375.88 kPa
C. 385.88 kPa
D. 395.88 kPa

Answer :

a. 365.88 kpa is the intercooler pressure between the 2nd and 3rd stage of the 3-stage air compressor.

Given:

Initial Pressure [tex]P_1 = 100 \, \text{kPa}[/tex]

Final Pressure [tex]P_3 = 700 \, \text{kPa}[/tex]

The steps are:

  • Let's assume that the pressure increase ratio is the same for each stage:

[tex](\frac{P_2}{P_1} = \frac{P_3}{P_2})[/tex]

  • Since there are 3 stages, the pressure increase ratio for each stage is given by:

[tex]\left(\frac{P_3}{P_1}\right)^{\frac{1}{3}} = \frac{P_2}{P_1}[/tex]

  • Substituting the given values:

[tex]\left(\frac{700}{100}\right)^{\frac{1}{3}} = \frac{P_2}{100}[/tex]

[tex](7)^{\frac{1}{3}} = \frac{P_2}{100}[/tex]

  • Calculating [tex](7)^{\frac{1}{3}}[/tex] gives approximately 1.9129. Then:

[tex]1.9129 = \frac{P_2}{100}[/tex]

[tex]P_2 = 100 \times 1.9129 = 191.29 \, \text{kPa}[/tex]

  • We continue this process to step up to the final stage where [tex]P_2[/tex] becomes [tex]P_2 \, \times (7)^{1/3}[/tex] and equate it:

[tex]P_2 = 191.29 \, \times 1.9129
\approx 365.88 \, \text{kPa}[/tex]

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Rewritten by : Barada