Abstract: Energy expenditure of the meridian system in traditional Chinese medicine (TCM) for living human bodies is one of the fundamental questions regarding the physical properties of the meridian system. As a first attempt to address this, 24 hand/foot meridians were modeled as a continuous channel with the sustainable movement of Qi and blood inside. Then, the fluid mechanics energy equation for steady and incompressible flow was applied to estimate the pumping power of meridian circulation, based on the meridian length, blood viscosity and circulation velocity. Additional findings based on the pumping power estimation results include: (1) new information to corroborate the determination of the production era of Yellow Emperor’s Inner Classics (Huang Di Nei Jing, 《黄帝内经》); (2) a new definition for work of breathing (WOB) from a TCM perspective. This paper could lead to future research aimed at modernizing the understanding of the meridian system, Qi and TCM using quantitative methods.