A noninvasive method for estimating 2-D pressure gradients from ultrasound vector velocity data is presented. It relies on vector velocity fields acquired using the transverse oscillation method during steady flow conditions. The pressure gradients are calculated from the velocity fields using the Navier-Stokes equations. Scans of a carotid bifurcation phantom with a 70% constriction are performed using a linear transducer connected to a scanner. The performance of the estimator is evaluated by comparing its results to those of a computational fluid dynamics model of the carotid bifurcation phantom. The geometry of the model is determined from magnetic resonance imaging. The presented study is conducted assuming steady flow using velocity data acquired at 18 frames per second. The proposed method shows pressure gradients at the constricted region from -8 kPa/m to 9 kPa/m, with a maximum bias of -7% for the axial component and -8% for the lateral component. The relative standard deviation of the estimator is 5% (axial component) and 30% (lateral component) when studying the pressure gradient across the constriction using 3 velocity frames per pressure estimate. The study shows that 2-D pressure gradients can be achieved noninvasively using ultrasound data in a constant flow environment.