This paper presents the application of an economic model predictive control (MPC) for the operational management of water distribution networks (WDNs) with periodic operation and nonlinear constraint relaxation. In addition to minimizing operational costs, the proposed approach aims to reduce the computational load and to improve the implementation efficiency associated with the nonlinear nature of the MPC problem. The behavior of the WDN is characterized by a set of difference-algebraic equations, where the relation of hydraulic pressure/head and flow in interconnected pipes is nonlinear. Specifically, the considered WDN model includes two categories of nonlinear algebraic equations for unidirectional and bidirectional flows in pipes, respectively. In this paper, we propose an iterative algorithm to relax these nonlinear algebraic equations into a set of linear inequality constraints that will be implemented in the economic MPC design, which improves the implementation efficiency and meanwhile optimizes the economic performance. Finally, the proposed strategy is applied to a well-known benchmark of the Richmond WDN. The closed-loop simulation results are shown and the proposed strategy is also compared with a nonlinear economic MPC using several key performance indexes.