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Q: A 6-in.-OD pipe is buried with its centerline 50 in. below the surface of the ground [k of soil is 0.20 Btu/(h ft °F)]. An oil having a density of 6.7 lb/gal and a specific heat of 0.5 Btu/(lb °F) flows in the pipe at 100 gpm. Assuming a ground surface temperature of 40°F and a pipe wall temperature of 200°F, estimate the length of pipe in which the oil temperature decreases by 10°F.
GIVEN
An oil filled pipe buried below the surface of the ground
Pipe outside diameter (D) = 6 in. = 0.5 ft
Depth of centerline (z) = 50 in.
Thermal conductivity of the soil (k) = 0.20 Btu/h ft °F
Specific gravity of oil (Sp. Gr.) = 0.8
Specific heat of oil (cp) = 0.5 Btu/lb °F
Flows rate of oil mi= 100 gpm
The ground surface temperature (Ts) = 40°F
The pipe wall temperature (Tp) = 200°F
ASSUMPTIONS
Steady state condition
Two dimensional heattransfer
