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Water Distribution Networks are a particularly critical infrastructure for the high energy costs and frequent failures. Variable Speed Pumps have been introduced to improve the regulation of water pumps, a key for the overall infrastructure performance. This paper addresses the problem of analyzing the effect of the VSPs regulation on the pressure distribution of a WDN, which is highly correlated to leakages and energy costs. Due to the fact that water network behavior can only be simulated, we formulate the problem as a black box feasibility determination, which we solve with a novel stochastic partitioning algorithm, the Feasibility Set Approximation Probabilistic Branch and Bound, that extends the algorithm previously proposed by two of the authors. We use, as black box, EPANet, a widely adopted hydraulic simulator. The preliminary results, over theoretical functions as well as a water distribution network benchmark case, show the viability and advantages of the proposed approach.