In order to investigate the reliability of the so called mean velocity/vessel area formula adopted in clinical practice for the estimation of the flow rate using an intravascular Doppler guide wire instrumentation, a multiscale computational model was used to give detailed predictions on flow profiles within Y-shaped coronary artery bypass graft (CABG) models. At this purpose three CABG models were built from clinical patient's data and used to evaluate and compare, in each model, the computed flow rate and the flow rate estimated according to the assumption of parabolic velocity profile. A consistent difference between the exact and the estimated value of the flow rate was found in every branch of all the graft models. In this study we showed that this discrepancy in the flow rate estimation is coherent to the theory of Womersley regarding spatial velocity profiles in unsteady flow conditions. In particular this work put in evidence that the error in flow rate estimation can be reduced by using the estimation formula recently proposed by Ponzini et al. [Ponzini R, Vergara C, Redaelli A, Veneziani A. Reliable CFD-based estimation of flow rate in haemodynamics measures. Ultrasound Med Biol 2006;32(10):1545-55], accounting for the unsteady nature of blood, applicable in the clinical practice without resorting to further measurements.