Trade-off between shunt current loss and pumping loss is a major challenge in the design of the electrolyte piping network in a flow battery system. It is generally recognized that longer and thinner ducts are beneficial to reduce shunt current but detrimental to minimize pumping power. Base on the developed analog circuit model and the flow network model, we make case studies of multi-stack vanadium flow battery piping systems and demonstrate that both shunt current and electrolyte flow resistance can be simultaneously minimized by using longer and thicker ducts in the piping network. However, extremely long and/or thick ducts lead to a bulky system and may be prohibited by the stack structure. Accordingly, the intrinsic design trade-off is between system efficiency and compactness. Since multi-stack configurations bring both flexibility and complexity to the design process, we perform systematic comparisons among representative piping system designs to illustrate the complicated trade-offs among numerous parameters including stack number, intra-stack channel resistance and inter-stack pipe resistance. As the final design depends on various technical and economical requirements, this paper aims to provide guidelines rather than solutions for designers to locate the optimal trade-off points according to their specific cases.