A major determinant of the success of surgical vascular modifications, such as the total cavopulmonary connection (TCPC), is the energetic efficiency that is assessed by calculating the mechanical energy loss of blood flow through the new connection. Currently, however, to determine the energy loss, invasive pressure measurements are necessary. Therefore, this study evaluated the feasibility of the viscous dissipation (VD) method, which has the potential to provide the energy loss without the need for invasive pressure measurements. Two experimental phantoms, a U-shaped tube and a glass TCPC, were scanned in a magnetic resonance (MR) imaging scanner and the images were used to construct computational models of both geometries. MR phase velocity mapping (PVM) acquisitions of all three spatial components of the fluid velocity were made in both phantoms and the VD was calculated. VD results from MR PVM experiments were compared with VD results from computational fluid dynamics (CFD) simulations on the image-based computational models. The results showed an overall agreement between MR PVM and CFD. There was a similar ascending tendency in the VD values as the image spatial resolution increased. The most accurate computations of the energy loss were achieved for a CFD grid density that was too high for MR to achieve under current MR system capabilities (in-plane pixel size of less than 0.4 mm). Nevertheless, the agreement between the MR PVM and the CFD VD results under the same resolution settings suggests that the VD method implemented with a clinical imaging modality such as MR has good potential to quantify the energy loss in vascular geometries such as the TCPC.