The effects of non-uniform drifting plasmas (in presheaths) on planar Langmuir probes and Mach probes are investigated in an unmagnetized argon plasma. Mach probe data are compared with double-sided Langmuir probe data. The calculated plasma potential from the Langmuir probe is found to be approximately equal to the average of the plasma potentials calculated from data on each side of the Mach probe. A new method is presented to determine the ion drift velocity using the electron saturation currents for u(m) < 1 where u(m) is the Mach number. This approach has the advantage that it uses much higher currents. It is shown that a single-sided planar probe gives information about the plasma almost an ion-neutral collision length away from the probe and should not be used in drifting plasma. The one-sided Langmuir probe on the downstream side of the Mach probe indicates the plasma potential where the ion drift velocity is zero and a one-sided Langmuir probe on the upstream side of the Mach probe also indicates the plasma potential where the ion drift velocity is zero.