Real-time control of urban drainage networks requires knowledge about stored volumes and flows in order to predict overflows and optimize system operation. However, using flow sensors inside the pipelines means prohibitively high installation and maintenance costs. In this article, we formulate two nonlinear, constrained estimation problems for identifying the open-channel flow in urban drainage networks. To this end, we distribute cost-efficient level sensors along the pipelines and formulate the estimation problems based on the spatiallydiscretized kinematic and diffusion wave approximations of the full Saint-Venant partial differential equations. To evaluate the capabilities of the two models, the two approaches are compared and evaluated on modeling a typical phenomenon occurring in drainage systems: the backwater effect. An extensive realworld experiment demonstrates the effectiveness of the two approaches in obtaining the model parameters on a scaled water laboratory setup, in the presence of measurement noise.