This work deals with the hydraulic gradient estimation in real-time of a transport pipeline computational model by considering a slightly compressible fluid and slightly deformable conduit walls. Since the hydraulic gradient (J(Q)) caused by the friction phenomenon in a pipeline plays an important role in the system's behavior, and this function is affected by fluid properties' deviations, environmental disturbances and conduit deteriorations, it is proposed that the on-line estimation of J(Q) could be part of a monitoring system. The proposition can be applied to obtain computational models of a line with a junction and assumes only measurements of pressure and flow rate at the ends of the conduit and the junction outflow. The generic form of the gradient function J(Q) is a second-order polynomial with coefficients that involve indirectly pipe roughness, the transversal area of the conduit, fluid viscosity and elements connected to the line. The extended Kalman filter (EKF) is applied to estimate the coefficients of the function J(Q). As a test apparatus, a 163 m long hydraulic pipeline is used. Diverse experiments show the usefulness of the on-line estimation of J(Q) for monitoring and simulation tasks where computational models are necessary.