Doppler ultrasound is a non-invasive imaging technique that measures blood flow velocity and is commonly used in cardiac evaluation and vascular assessment. Compared to the conventional longitudinal view, cross-sectional Doppler is more robust to motion, making it more suitable for monitoring applications. In this paper, an adaptive framework is presented to automatically monitor flow in the common carotid artery using cross-sectional Doppler. Based on a vessel segmentation and geometry estimation, transmit parameters such as the focal point, steering angle and aperture width are adaptively adjusted to optimize the Doppler angle and to maximize SNR. The velocity profile is estimated using multiple gates along a single line, resulting in velocity estimates with high temporal resolution. The effect and optimal settings of relevant non-adaptive ultrasound parameters is explored through a design of experiments, making use of simulated and phantom data. These optimal parameters result in accurate estimates of average velocity with a mean error of 0.8% in silico and 1.6% in vitro. In addition, velocity estimates show a reduced variance and improved temporal resolution compared to conventional line-by-line scanning. Feasibility of the method is also demonstrated in vivo, where a diverse range of velocity profiles was observed. These findings suggest that this method could be feasible for automatic flow monitoring or cardiac output estimation through hemodynamic modeling.