In this work we analyze the effects of inherent random noise on the detectability of low-contrast vessel structures that possess slow flow. When flow is encoded in more than one direction, the number of independent noise contributions increases in addition to the scan time. In a fast-flow scenario, only the noise contribution from sampling along the direction of flow is of any significance. At slow flow rates, however, it becomes necessary to account for the noise in each encoded Cartesian direction. The degree to which noise affects low-contrast detectability also depends on the method of phase contrast image processing employed. A theoretical analysis of the statistical properties of signal and noise in processed phase contrast magnitude images is presented and verified from experimental MR image data. Results show a progressively increased bias in the processed phase contrast image magnitude at slow flow rates due to contributions from inherent random noise. The amount of this bias increases with the number of physical directions in which flow is encoded and is larger for complex difference processed images than for phase difference processing. Correspondingly, the output signal-to-noise ratio associated with flow is compromised.