  In this paper we use radio polarimetric observations of the jet of the nearby
bright quasar 3C\,345 to estimate the fluid velocity on kiloparsec scales. The
jet is highly polarized, and surprisingly, the electric vector position angles
in the jet are ``twisted'' with respect to the jet axis. Simple models of
magnetized jets are investigated in order to study various possible origins of
the electric vector distribution. In a cylindrically-symmetric transparent jet
a helical magnetic field will appear either transverse or longitudinal due to
partial cancellations of Stokes parameters between the front and back of the
jet. Synchrotron opacity can break the symmetry, but it leads to fractional
polarization less than that observed, and to strong frequency dependence that
is not seen. Modeling shows that differential Doppler boosting in a diverging
jet can break the symmetry, allowing a helical magnetic field to produce a
twisted electric vector pattern. Constraints on the jet inclination, magnetic
field properties, intrinsic opening angle, and fluid velocities are obtained,
and show that highly relativistic speeds ($\beta \ga 0.95$) are required. This
is consistent with the observed jet opening angle, with the absence of a
counter-jet, with the polarization of the knots at the end of the jet, and with
some inverse-Compton models for the X-ray emission from the 3C\,345 jet. This
model can also apply on parsec scales and may help explain those sources where
the electric vector position angles in the jet are neither parallel nor
transverse to the jet axis.
