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The suction condition of an air compressor is 98 kPa, 27ºC, and 0.2 m³/sec. If the surrounding air is 100 kPa and 20ºC, determine the free air capacity in m³/sec.

Answer :

The free air capacity of the air compressor is approximately [tex]0.1914 \text{ m}^3/\text{s}[/tex].

  • The given conditions of the compressor are:

Suction pressure = 98 kPa

Suction temperature = 27°C

Suction volume flow rate = 0.2 m³/s

  • The conditions of the free air (surrounding environment) are:

Free air pressure = 100 kPa

Free air temperature = 20°C

  • The free air capacity can be found using the equation:

[tex]\text{Free Air Capacity (FAC)} = \left( \frac{P_{suction}}{P_{free}} \right) \left( \frac{T_{free} + 273}{T_{suction} + 273} \right) \times \text{Suction Volume Flow Rate}[/tex]

  • Where:

[tex]P_{suction}[/tex] is the pressure at the suction conditions (98 kPa)

[tex]P_{free}[/tex] is the free air pressure (100 kPa)

[tex]T_{suction}[/tex] is the suction temperature (27°C converted to Kelvin)

[tex]T_{free}[/tex] is the free air temperature (20°C converted to Kelvin)

  • Convert the temperatures to Kelvin:

[tex]T_{suction} = 27 + 273 = 300 \text{ K}[/tex]

[tex]T_{free} = 20 + 273 = 293 \text{ K}[/tex]

  • Substitute the values into the equation:

[tex]\text{FAC} = \left( \frac{98}{100} \right) \left( \frac{293}{300} \right) \times 0.2[/tex]

  • Calculate the free air capacity:

[tex]\text{FAC} = 0.98 \times 0.9767 \times 0.2[/tex]

[tex]\approx 0.1914 \text{ m}^3/\text{s}[/tex]

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