Abstract: The investigation of frictional pressure drops in wire-wrapped bundles at low flow velocities is crucial for thermal-hydraulic studies of sodium-cooled fast reactor cores. This study aims to refine empirical formulas for predicting friction factors in wire-wrapped bundles by addressing their limitations in accurately calculating friction factors during transition regime. By analyzing existing empirical formulas and meticulously observing frictional pressure drop experiments conducted under low-flow conditions that reported in the literature, the study proposes and demonstrates the mechanism of the laminar-to-transitional regime transition in wire-wrapped bundles. Additionally, experimental research was conducted on the frictional pressure drop of a 37-rod wire-wrapped bundle. A novel high-precision differential pressure measurement technique, the photographic liquid column manometer, was employed to enhance frictional pressure drop measurement accuracy. This innovative method achieves a measurement uncertainty of less than 2 Pa within a range of 0 to 300 Pa. The mass flow rate of the fluid was measured and converted to obtain the flow velocity through the assembly, further improving the accuracy of flow velocity measurements. The analysis and experiments reveal that the transition from the laminar to transitional regime does not occur uniformly but initiates locally in certain subchannels before spreading across the assembly as flow velocity increases. Significant increases in the frictional pressure drop occur only after a sufficient number of subchannels have undergone transition. This perspective is supported by extensive existing literature, which report that in assemblies with fewer rod bundles, smaller P/D and H/D values, and constructed from hard metal materials such as stainless steel, the friction factor at the initial stage of the transitional regime shows a significant increase or remains constant with increasing Reynolds number. Under these conditions, the high consistency of the P/D ratio within the assembly causes the fluid to transition within a narrow range of flow velocities, leading to a marked increase in the friction factor with Reynolds number. The research results also indicate that the prediction accuracy of the critical Reynolds number for the laminar-to-transitional flow transition significantly impacts the calculation accuracy of empirical formulas at low flow velocities. Formulas using smaller predicted values of the critical Reynolds number show better agreement between predicted values and the measured results in this study. Therefore, the study recommends adopting smaller critical Reynolds numbers and interpolation indices in empirical formulas to facilitate an early onset and smooth transition of laminar-to-transitional regime behavior in friction factors, thereby improving the accuracy of calculated friction factors.