In this paper, we present a self-sustainable sensor network model for integrity monitoring of pipeline infrastructures. Sensor nodes consist of energy harvesting modules which help them to be always alive and hence monitor the pipeline continuously. These nodes report in a multi-hop fashion to more expensive sink nodes that can broadcast to the base station. The main objective of the paper is to compute the minimal number of sinks required to keep the network connected and satisfy the required constraints. Firstly, we present an algorithm (CON-NET) for determining if a network is connected. We propose a modified bisection algorithm to compute the maximum sampling rate for a given number of sinks nodes. Further, we propose an algorithm for computing the minimal number of sink nodes required. We illustrate the use of algorithms by providing design guidelines for a sensor network on a linear pipeline structure.