  We apply the lubrication approximation to solve for the flow generated by a
peristaltic traveling wave in a finite, planar channel, and examine the effect
of channel length. Cerebrospinal fluid (CSF) is hypothesized to be
peristaltically transported by arterial pulsations through the perivascular
spaces in the brain. Previous studies of peristaltic perivascular models have
chosen model lengths ranging from sub-wavelength, which is more physiologically
realistic, to full wavelength. Here, we solve for peristaltic flow rates for
arbitrary lengths, and find that sub-wavelength channels significantly modulate
the mean value, phase, and amplitude of flow rate for sinusoidal and general
peristaltic waveforms. The boundary conditions create an internal pressure
gradient such that the instantaneous flow rate varies along the length of the
channel, and the difference between the ends and the middle of the channel is
more pronounced for very short channels. This longitudinal distribution in flow
rate is not observed \emph{in vivo} in perivascular spaces at the surface of
the brain, and hence sub-wavelength peristaltic models whose boundary
conditions are isolated from the larger perivascular network are limited in
their ability to reproduce perivascular flows.
