A Tesla valve is a kind of micro-valve without moving parts. Due to the great difference between the reverse and forward flow, the Tesla valve is often used in passive fluid control devices. However, most of the current Tesla valve components are optimized and designed based on asymmetric structures. In this study, a Tesla valve pipe system model with symmetric structure is proposed. The characteristics of fluid flow and pressure drop were studied by finite element method and dimensional analysis. First, the pressure drop characteristics of symmetric and asymmetric Tesla valves with different Reynolds number are considered. The results show that the better the symmetry, the better the one-direction flow characteristics of Tesla valve system. Afterwards, through parametric analysis, computational fluid dynamics was used to verify flow characteristics of completely symmetrical Tesla valve system. The shunt angle, shunt pipe diameter and number of valves have significant effects on the pressure drop characteristics of the system. Eventually, based on numerical simulation results, by using the dimensional analysis method, the modification parameter $\alpha (\alpha =\alpha (\theta ,d,N))$ was introduced to obtain the scaling law $\mathrm{\Delta }p\sim (1+\ln (1+N^{3/5R{e}^{1/3}}))\rho V^{2}L{D}^{-1}R{e}^{-1/4}$ between the pressure drop and other parameters of the completely symmetrical Tesla valve piping system.