The effect of phase angle between pressure and flow waveforms on the flow characteristics in stenosed compliant vessels for coronary (phase angle (PA) of approximately ) and peripheral flows (PA of approximately ) is investigated using time resolved digital particle image velocimetry. Synthetic arteries with 50% and 75% stenosis at various physiological conditions with Reynolds numbers (Re) of 250, 350, and 450 and corresponding Womersley parameter of 2.7, 3.2, and 3.7 were studied; wall-shear stresses (WSSs), oscillatory shear index (OSI), and recirculation lengths were determined. Additionally, flow transitional characteristics were examined using power spectral density (PSD), wavenumber spectra, and turbulence statistics of the axial velocity component. It is observed that the coronary flow conditions exhibit lower wall-shear stresses and larger recirculation lengths compared with peripheral flows. Mean peak shear stresses can be as high as and for peripheral and coronary flows, respectively, with 50% stenosis at and . These values can be as high as and , respectively, for the same conditions with 75% stenosis. The OSI is close to 0.5 near the reattachment point indicating fluctuating WSS over the entire cardiac cycle for both 50% and 75% stenosis. For 50% stenosis, the OSI fluctuated at various locations over the length of the vessel indicating several regions of recirculation in contrast to a distinct recirculation region observed for 75% stenosis. PSD plots across various cross-sections along the length of the vessel and wavenumber spectra along the centerline indicate that turbulence occurs only for 75% stenosis. For coronary flows, the streamwise locations where the flow transitions to turbulence and relaminarizes are approximately one diameter upstream compared with peripheral flows indicating that coronary flows are more susceptible to turbulence.