A cylindrical heat exchanger is used to warm up a stream of 0.15 kg s−1 cold air from a temperature of 200 K to 300 K, after which it is released into the atmosphere. The air enters and leaves the heat exchanger through a pipe with a diameter of 5 cm. The heat exchanger is of a “shell and tube” design ; the air flows through the inside of the tubes. The internal diameter of the shell is 40 cm. There are 40 tubes each with a diameter of 1 cm in the heat exchanger.
It can be assumed that there is no friction in the system. The only changes in the gas
density occur inside the tubes; elsewhere, the gas can be considered incompressible. The density of the air at 300 K is 1.23 kg m−3. The viscosity of air at 200 K is 1.1 10 kg m s; at 300 K it is 1.8 10 kg m s
a) Estimate the density of air at 200 K. [2 marks]
b) Calculate the gas volumetric flow rates at points A and F. [4 marks]
c) Determine whether the air flow through the tubes is laminar or turbulent; perform this calculation at the beginning as well as the end of the tubes. [4 marks]
d) Determine the pressure at A. [7 marks]
e) Determine the pressures at B and E. [8 marks]
It can be assumed that there is no friction in the system. The only changes in the gas
density occur inside the tubes; elsewhere, the gas can be considered incompressible. The density of the air at 300 K is 1.23 kg m−3. The viscosity of air at 200 K is 1.1 10 kg m s; at 300 K it is 1.8 10 kg m s
a) Estimate the density of air at 200 K. [2 marks]
b) Calculate the gas volumetric flow rates at points A and F. [4 marks]
c) Determine whether the air flow through the tubes is laminar or turbulent; perform this calculation at the beginning as well as the end of the tubes. [4 marks]
d) Determine the pressure at A. [7 marks]
e) Determine the pressures at B and E. [8 marks]
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A)
P1V1/T1=P2V2/T2
P1T1/T2= (1.23)*(300/200)=1.845 kgm-3
B)
QA = 0.15/1.845 = 0.0813 m3 s−1 at 200 K
QF = 0.15/1.23 = 0.122 m3 s−1 at 300 K
c) flow is TURBULANT
Flow through each individual tube is Q/N
Velocity is Q/N/A
A= (0.01) 7.855 10-5 m
d) Pressure = 1.54 x10-4 Pascals
e) all pressures are absolute
Flow rate 0.081301 0.081301 0.081301 0.121951 0.121951 0.121951
Diameter 0.05 0.4 0.01 0.01 0.4 0.05
Area 0.002026 0.129663 0.003242 0.003242 0.129663 0.002026
Velocity 40.12898 0.627015 25.08061 37.62092 0.940523 60.19347
Pressure 1.54E+05 1.55E+05 1.55E+05 1.03E+05 1.04E+05 1.01E+05
Re Re
4.21E+04 2.57E+04
P1V1/T1=P2V2/T2
P1T1/T2= (1.23)*(300/200)=1.845 kgm-3
B)
QA = 0.15/1.845 = 0.0813 m3 s−1 at 200 K
QF = 0.15/1.23 = 0.122 m3 s−1 at 300 K
c) flow is TURBULANT
Flow through each individual tube is Q/N
Velocity is Q/N/A
A= (0.01) 7.855 10-5 m
d) Pressure = 1.54 x10-4 Pascals
e) all pressures are absolute
Flow rate 0.081301 0.081301 0.081301 0.121951 0.121951 0.121951
Diameter 0.05 0.4 0.01 0.01 0.4 0.05
Area 0.002026 0.129663 0.003242 0.003242 0.129663 0.002026
Velocity 40.12898 0.627015 25.08061 37.62092 0.940523 60.19347
Pressure 1.54E+05 1.55E+05 1.55E+05 1.03E+05 1.04E+05 1.01E+05
Re Re
4.21E+04 2.57E+04