The Fontan operation is one in which the right heart is bypassed leaving the left ventricle to drive the blood through both the capillaries and the lungs, making it important to design an operation which is hemodynamically efficient. The object here was to relate the pressure in Fontan connections to its geometry with the aim of increasing the hemodynamically efficiency. From CT or magnetic resonance images, glass models were made of realistic atrio-pulmonary (AP) and cavo-pulmonary (CP) connections in which the right atrium and/or ventricle are bypassed. The glass models were connected to a steady flow loop and flow visualization, pressure and 3 component LDA measurements made. In the AP model the large atrium and curvature of the conduit created swirling patterns, the magnitude of which was similar to the axial velocity. This led to an inefficient flow and a subsequent large pressure loss (780 Pa). In contrast, the CP connection with a small intra-atrial chamber had reduced swirling and a significantly smaller pressure loss (400 Pa at 8 l.min) and was therefore a more efficient connection. There were, however, still pressure losses and it was found that these occurred where there was a large bending of the flow, such as from the superior vena cava to the MPA and from the MPA to the right pulmonary artery.