A long, 2-cm-diameter horizontal copper pipe carries dry saturated steam at 120 kPa absolute pressure. The pipe is contained within an environmental testing chamber in which the ambient air pressure can be adjusted from 50 kPa to 200 kPa absolute, while the ambient air temperature is held constant at 20°C. What is the effect of this pressure change on the rate of condensate flow per meter length of pipe? Assume that the pressure change does not affect the absolute viscosity, thermal conductivity, or specific heat of the air.
GIVEN
• A long horizontal copper pipe carrying saturated steam within an environmental testing chamber
• Outside diameter (D) = 2 cm = 0.02 m
• Steam pressure = 120 kPa
• Ambient pressure range (P) = 50 to 200 kPa
• Ambient air temperature (T?) = 20°C FIND
• Effect of ambient pressure change on rate of condensate flow per meter length of pipe
ASSUMPTIONS
• Pressure change has no effect on absolute viscosity, thermal conductivity, or specific heat of the air
• Air is still
• Chamber temperature is held constant while pressure is changed
• Convective thermal resistance on the inside of the pipe is negligible
• Thermal resistance of the copper pipe is negligible
• The air behaves as an ideal gas
SKETCH
PROPERTIES AND CONSTANTS
For saturated steam 0.12 MPa the heat of vaporization (hfg) = 2238 kJ/kg, and the temperature (Ts) = 105°C.
for dry air at the mean temperature of 62.5°C and one atmosphere
Thermal expansion coefficient (?) = 0.00298 1/K
Thermal conductivity (k) = 0.0281 W/(m K)
Absolute viscosity (?) = 20.02 × 10–6 (N s)/m2
Prandtl number (Pr) = 0.71
Density (?) = 1.018 kg/m3
For an ideal gas 12PP = 12
The Grashof number based on the pipe diameter is
The Nusselt number for a horizontal cylinder is given by (All requirements are satisfied at both pressures.)
The rate of heat transfer per meter length of pipe is
It is clear that raising the ambient pressure from 50 kPa to 200 kPa will double the flow of condensation ( m c)per meter of pipe
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