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Determine the optimum economic thickness of insulation that should be used under the following conditions: Saturated steam is being passed continuously through a steel pipe with an outside diameter of 10.75 in. The temperature of the steam is 400"F, and the steam is valued at $1.80 per 1000 lb. The pipe is to be insulated with a material that has a thermal conductivity of 0.03 Btu/(h)(ft2)(°F/ft). The cost of the installed insulation per foot of pipe length is $4.5 x It where It, is the thickness of the insulation in inches. Annual fixed charges including maintenance amount to 20 percent of the initial installed cost. The total length of the pipe is 1000 ft, and the average temperature of the surroundings may be taken as 70°F. Heat-transfer resistances due to the steam film, scale, and pipe wall are negligible. The air-film coefficient at the outside of the insulation may be assumed constant at 2.0 Btu/(h)(ft2)(°F) for all insulation thicknesses
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