Blood flow velocities can be measured using a Doppler flow wire. This numerical study evaluates the impact of a 0.014" flow wire on the measured frequencies in a straight artery with diameters of 3 mm and 4 mm, under steady and pulsatile flow conditions. Simulations were performed with the wires positioned differently in the artery (perfectly centred and at an offset of 0.5 mm from the wall) and with different types of wire (tilted and straight). Measurements were taken at range gates from 4 mm to 10 mm. During simulations using a 3-mm vessel under pulsatile flow conditions, the relative error between the measured and reference maximum frequency (occurring in absence of the wire) decreased from 17.7% to 11.6% (with a mean value of 14.9%). During simulations using an off-centre 1.5 degree tilted wire, the mean error was approximately 5%. Therefore, our study suggests that that a centrally positioned flow wire is unfavourable for measuring flow velocities.