This article addresses the design problems associated with pipe networks in cooling water systems. The objective is to determine the lowest cost network that can supply the heat exchangers with cooling water at the flow rates previously established in the thermal design. The solution to the problem provides the diameter for each section of pipe in the network together with the corresponding pump alternative. The objective function and constraints are organized in a matrix formulation where the solution consists of a set of linear programming problems. The basic structure of the optimal design problem also extends to the solution for revamp problems. The comparison of the proposed approach to the traditional solution based on economical velocities indicates that the optimization scheme can make pipe network designs less expensive and more reliable for supplying cooling water.