## Most Economical Diameter

We have seen how to determine the driving force (e.g., pumping requirement) for a given pipe size and specified flow as well as how to determine the proper pipe size for a given driving force (e.g., pump head) and specified flow. However, when we install a pipeline or piping system we are usually free to select both the "best" pipe and the "best" pump. The term "best" in this case refers to that combination of pipe and pump that will minimize the total system cost.

The total cost of a pipeline or piping system includes the capital cost of both the pipe and pumps as well as operating costs, i.e. the cost of the energy required to drive the pumps:

Capital cost of pipe (CCP) Capital cost of pump stations (CCPS) Energy cost to power pumps (EC)

Although the energy cost is "continuous" and the capital costs are "one time,'' it is common to spread out (or amortize) the capital cost over a period of Y years i.e., over the "economic lifetime'' of the pipeline. The reciprocal of this (X = 1/ Y) is the fraction of the total capital cost written off per year. Taking 1 year as the time basis, we can combine the capital cost per year and the energy cost per year to get the total cost (there are other costs, such as maintenance, but these are minor and do not materially influence the result).

Data on the cost of typical pipeline installations of various sizes were reported by Darby and Melson (1982). They showed that these data can be represented by the equation:

where Dft is the pipe ID in feet, and the parameters a and p depend upon the pipe wall thickness as shown in Table 7-2. Likewise, the capital cost of (installed) pump stations (for 500 hp and over) was shown to be a linear function of the pump power, as follows (see Fig. 7-4):

where A = 172, 800, B = 450.8hp-1 (in 1980 \$), and HP/% is the horsepower rating of the pump, (HP is the "hydraulic power,'' which is the power delivered directly to the fluid).

The energy cost is determined from the pumping energy requirement, which is in turn determined from the Bernoulli equation:

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