Compare the rate of condensate flow from the pipe in Problem 8.28 (air pressure = 200 kPa) with that for a 3.89-cm-OD pipe and 200 kPa air pressure. What is the rate of condensate flow if the 2 cm pipe is submerged in a 20°C constant-temperature water bath?

Question

GIVEN

• A long horizontal copper pipe carrying saturated steam within an environmental testing chamber or a water bath

• Steam pressure = 120 kPa

• Ambient pressure (P) = 2 atm

• Ambient air or water temperature (T?) = 20°C

FIND

Rate of condensate flow for

(a) Diameter (D) = 3.89 cm = 0.0389 m Fluid is air at 2.0 atm

(b) Diameter (D) = 2 cm = 0.02 m Fluid is water at T? = 20°C

ASSUMPTIONS

• Pressure change has no effect on absolute viscosity, thermal conductivity, or specific heat of the air

• Air is still

• 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 at 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)

Prandtl number (Pr) = 0.71 at P = 2.0 Atm,

Kinematic viscosity (?) = 9.83 × 10–6 Ns/m2

Answer 1

The Grashof number is



Both cases fall within the range of requirements for the use



The condensate flow rate per meter of pipe is given by



COMMENTS

The rate of condensate flow with a 2-cm-diameter pipe in air at 200 kPa. is 2.1 g/min. A change in the fluid from air to water leads to a much larger increase in the rate of condensate flow (100 times) than an increase in the pipe diameter to 3.89 cm (1.6 times).