In this paper, the frictional torques exerted on blades of turbine flowmeters are studied and described in some detail by means of boundary layer theory. A formula for calculating frictional torgues is obtained. The formula shows in laminal flow the frictional torques are proportional to 2/3th power of flow rate, and in turbulant flow, to 13/7th power of flow rate. Then anew mathematical model of turbine flowmeter is derived. The characteristic curves of the turbine flowmeter obtained from it is fully in agreement with the experimental data. A new concept about the critical Reynolds number of turbine flowmeters is also proposed in this paper. It can be used to judge the characteristic curves of the turbine flowmeter and choose the optimum design parameters of turbine flowmeters to increase the ratio of measurement range.