Air exits a compressor operating at steady-state, steady-flow conditions at 150°C, 825 kPa, with a velocity of 10 m/s through a circular pipe of 5.0 cm diameter.
(a) Determine the outlet volumetric flow rate and the mass flow rate of the air.
(b) If the air enters the compressor through an inlet at 20.0°C and 100. kPa, and a velocity of 1.0 m/s, determine the volumetric flow rate of the air entering the compressor and the required cross-sectional area of the inlet.
(c) Using your equations, plot the inlet volumetric flow rate and the inlet cross-sectional area as the inlet air velocity is varied between 0.25 m/s and 10.0 m/s.
Given: T2 = 150°C = 423 K; P2 = 825 kPa; V2 = 10 m/s; D2 = 5 cm = 0.05 m
What will be an ideal response?
(a) Assuming air is an ideal gas, with R = 0.287 kJ/kg-K: v2 = RT2/P2 = 0.1471 m3/s
A2 = ?D22/4 = 0.001963 m2
V?2=V2A2 = 0.0196 m3/s
m?=V?2/v2 = 0.133 kg/s
(b) The mass flow rate is constant for a steady-state, steady-flow compressor:
Given: T1 = 20°C = 293 K; P1 = 100 kPa; V1 = 1 m/s
Solution: v1 = RT1/P1 = 0.8409 m3/s
V1?=m?v1= 0.112 m3/s
A1=V?1/V1 = 0.112 m2
(c)
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