A DIMENSIONLESS THEORY FOR THE ECONOMIC DESIGN OF PRESSURIZED PIPES

B. ACHOUR, L. AMARA

Abstract


The economic design of pressurized pipes has traditionally been formulated as an optimization problem balancing capital investment against pumping energy expenditure. Although numerous computational techniques have been proposed for determining the optimum pipe diameter, the mathematical structure of the governing equations has received comparatively little attention. The present study revisits the classical problem from an analytical viewpoint by developing a rigorous dimensionless formulation based on the Darcy-Weisbach equation and the Colebrook-White resistance law.

A compound variable combining the Reynolds number and the Darcy-Weisbach friction factor is first introduced, followed by a systematic nondimensionalization of both the hydraulic and economic equations. This analytical procedure transforms the conventional optimization problem into a compact dimensionless framework governed by two reduced variables. It is further demonstrated that the investment and operating cost coefficients naturally combine into a single dimensionless economic parameter representing the relative contribution of energy expenditure with respect to capital investment. Consequently, the optimal design is shown to depend on the balance between these competing mechanisms rather than on their individual dimensional values.

The proposed formulation preserves the full hydraulic rigor of the Colebrook-White equation while considerably simplifying the mathematical structure of the optimization problem. Beyond its immediate application to pipe sizing, the resulting framework provides a clearer physical interpretation of the interaction between hydraulic resistance and economic performance, thereby establishing a unified analytical basis for the economic design of pressurized pipeline systems.


Keywords


Pressurized pipes, Economic optimization, Darcy-Weisbach equation, Colebrook-White equation, Dimensionless analysis, Dimensionless formulation, Hydraulic design, Life-cycle cost.

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References


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