This study concerns the optimal design and operation of produced water and urban water networks. The optimization formulations of these problems have inherent nonconvexity, making them hard to solve. We address a key source of nonconvexity and difficulty in solving these problems: the representation of frictional pressure changes across network nodes using nonlinear constraints, typically modeled by the Hazen-Williams equation. For the optimization of produced water networks, we analytically show the effectiveness of using a standard piecewise linear approximation to generate near-optimal solutions for the original problem for a general network. Computational results with real-world problems confirm the success of this approach in terms solution quality and runtime. However, in the context of urban water network design problems, we recognize the limitations of a direct piecewise-linear approximation and propose an alternative solution. In particular, we develop a general-purpose primal heuristic to handle MINLPs with nonlinearities in continuous variables. The heuristic solves a sequence of approximations, with successively smaller domains of continuous variables appearing in nonlinearities. High-quality primal solutions for problems from the literature are obtained, even outperforming the best-known solutions in three of the nine problem instances.