In this paper the viscous frictional torgues T_(fb) exerted on the blades of a turbine flowmeter are studied and described in details in terms of two-dimensional boundary layer theory. The driving torque T_d of turbine flowmeter is also presented by means of the two-dimensional cascade theory. The results of calculation indicate that the blade frictional torques have a magnitude equal to that of the driving torques. By using fluid flow theory the other retarding torques,i.e, rotor hub viscous frictional torques T_(fh), blade tip clearance drag torques T_(ft), bearing retarding torques T_(fi) and hub ends retarding terques T_(fe) are presented. It is shown that the rotor hub viscous frictional torques have a larger magnitude than the other retarding torques. The factor of a turbine flowmeter is obtained by virtue of the equilibrium equation. The calculation results of the meter factor are fully in agreement with the experimental data.