Background: Non-invasive imaging-based assessment of blood flow plays a critical role in evaluating heart function and structure. Computed Tomography (CT) is a widely-used imaging modality that can robustly evaluate cardiovascular anatomy and function, but direct methods to estimate blood flow velocity from movies of contrast evolution have not been developed. Purpose: This study evaluates the impact of CT imaging on Physics-Informed Neural Networks (PINN)-based flow estimation and proposes an improved framework, SinoFlow, which uses sinogram data directly to estimate blood flow. Methods: We generated pulsatile flow fields in an idealized 2D vessel bifurcation using computational fluid dynamics and simulated CT scans with varying gantry rotation speeds, tube currents, and pulse mode imaging settings. We compared the performance of PINN-based flow estimation using reconstructed images (ImageFlow) to SinoFlow. Results: SinoFlow significantly improved flow estimation performance by avoiding propagating errors introduced by filtered backprojection. SinoFlow was robust across all tested gantry rotation speeds and consistently produced lower mean squared error and velocity errors than ImageFlow. Additionally, SinoFlow was compatible with pulsed-mode imaging and maintained higher accuracy with shorter pulse widths. Conclusions: This study demonstrates the potential of SinoFlow for CT-based flow estimation, providing a more promising approach for non-invasive blood flow assessment. The findings aim to inform future applications of PINNs to CT images and provide a solution for image-based estimation, with reasonable acquisition parameters yielding accurate flow estimates.