Aims: This work presents a method and instrumentation to measure pressure-dependent intra-cardiac cycle variations in local blood pulse propagation velocity PWV(P) using Bramwell-Hill (BH) equation by incorporating Kelvin-Voigt type arterial viscoelastic modelling. Methods: A pilot in-vivo study was conducted to verify the functionality of the proposed technique. The carotid diameter and pressure waveforms (sampled at 1 kHz) were measured using our extensively validated image-free ultrasound technology ARTSENS and a calibrated tonometer respectively. PWV(P) was measured for individual cardiac cycles. Results: Measurement system captured high fidelity pressure and diameter signals. Employing the viscoelastic modelling, reliable elastic pressure-diameter relationship curves were obtained for evaluating PWV(P). The cycle-to-cycle measurements of PWV(P) exhibited repeatable trends. The systolic PWV (PWVs) was on an average 20% higher than diastolic PWV (PWVd). It was also observed that the group average PWVs and PWVd were higher for hypertensive subjects as compared to normotensive. Conclusion: The proposed technique reliably measures the intra-cardiac cycle variations in PWV(P) and addresses various key considerations associated with non-invasive implementation BH equation for the same.