Question

A pump delivers a power p kw to transfer q m3 /s of crude oil of density kg/m3 through a long-distance horizontal pipeline of length l m, with a friction factor ff. The installed cost of the pipeline is $c1dml (where m = 1.4) and that of the pumping station is $(c2 + c3p); both these costs are amortized over n years. Electricity costs $c4 per kwh and the pump has an efficiency . The values of c1, c2, c3, and c4 are known. The pump inlet and pipeline exit pressure are the same. If there are n hours in a year, prove that the optimum pipe diameter giving the lowest total annual cost is: 1/( 5) 3 4 1 3 2 5 32 ; = ; 1000 m f opt f q l nc c l c d where m n n if c1 = 2280, c2 = 95000, c3 = 175, c4 = 0.11, = 850, l = 50000, = 0.75, and ff = 0.0065, all in units consistent with the above, evaluate dopt for q = 0.2 m3 /s, and n = 10 years.

Answer 1

Answer:

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