Methane gas enters a compressor like that shown here at 200 kPa, 30 oC through a

Question

Methane gas enters a compressor like that shown here at 200 kPa, 30 oC through a 0.5 m-diameter inlet with a velocity of 30 m-s-1. It leaves through 0.5 m-diameter pipe at 265 kPa, 24.4 m-s-1


What is the mass flow rate of methane through this compressor? (kg/s)
What is the volume flow rate of methane at the compressor inlet? (m3/kg)
What is the volume flow rate of methane at the compressor outlet? (m3/kg)
What is the methane's specific volume at the compressor outlet? (m3/kg)
What is the methane's temperature at the compressor outlet? (K)

Explanation / Answer

a) mass flow rate = m_rate = .A.V

= density of methane = 0.66 kg/m3
A = Area of pipe = /4 x 0.52 = 0.19625 m^2

V+ Velocity = 30

m_rate = 0.66 x 0.19625 x 30 = 3.89 KG/s

b) Volume flow rate at inlet= A.V1 = 0.19625 x 30 = 5.8875 m^3/s

c) Volume flow rate at inlet = A.V2 = 0.19625 x 24.4 = 4.79 m^3/s

d) methane's specific volume at the compressor outlet = 4.79/m_rate = 4.79/3.89 = 1.23 m^3/Kg

e) Taking methane to be ideal gas:

P = x R methanex T

P = 265 Kpa

= 0.66 Kg/m^3

R methane = 0.52 Kj/Kg.K

265 = 0.66 x 0.52 x T

T = 772.7 K

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