1. A steady flow compressor is used to compress helium from 15 psia and 70°F at the inlet to 200 psia and 600°F at the outlet. The outlet area and velocity are 0.01ft2 and 100 ft/s, respectively, and the inlet velocity is 50 ft/s. Determine the mass flow rate and inlet area. [

a. The mass flow rate through the compressor = 0.07

b. The value of area at inlet =  0.1337

Explanation:

Pressure at inlet = 15 psia = 103.4 kpa

Temperature at inlet = 70 °F = 294.3 K

Pressure at outlet =  200 psia = 1378 kpa

Temperature at outlet = 600 °F = 588.7 K

outlet area = 0.01 = 0.00093

Outlet velocity = 100 = 30.48

Inlet velocity = 50 = 15.24

Gas constant for helium R =2.077

(a). Mass flow rate is given by the formula  m = × × -------- (1)

Where is density at outlet. it is calculated by

⇒ =

⇒ = ×

⇒ = 1.127

Put the value of in equation ( 1 ) we get

Mass flow rate m = 1.127 × 0.00093 × 30.48

⇒ m = 0.032

⇒ m = 0.07

This is the mass flow rate through the compressor.

(b). Mass flow rate is constant through the compressor so it is also given by

⇒ m = × × ----------- ( 2 )

⇒ =

Put all the values in above formula we get

⇒ = ×

⇒ = 0.169

Put this value of in equation ( 2 ) we get,

⇒ m = 0.169 × × 15.24

⇒ 0.032 = 0.169 × × 15.24

⇒ = 0.01242 = 0.1337

This is the value of area at inlet.

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