  Supernova remnant (SNR) RX J1713.7-3946 is well known for its bright TeV
gamma-ray emission with shell-like morphology. To constrain the hydrodynamical
evolution, we have performed six times observations of the northwestern (NW)
shell with the Chandra X-ray Observatory from 2005 to 2011, and measured the
proper motion by using these data and the first epoch observation taken in
2000. The blast-wave shock speed at the NW shell is measured to be $(3900\pm
300) (d/{\rm kpc})\ {\rm km}\ {\rm s}^{-1}$ with an estimated distance of $d =
1$ kpc, and the proper motions of other structures within the NW shell are
significantly less than that. Assuming that the measured blast-wave shock speed
is the representative of the remnant's outer shock wave as a whole, we have
confronted our measurements as well as a recent detection of thermal X-ray
lines, with the analytic solution of the hydrodynamical properties of SNRs. Our
hydrodynamical analysis indicates that the age of the remnant is 1580-2100
years, supporting the association with SN393. A model with SN kinetic energy of
$E = 10^{51}\, \rm erg$, the ejecta mass of $M_{\rm ej} = 3\, M_{\odot}$, and
the ambient density at the current blast wave location of $n_2 = 0.015\, {\rm
cm}^{-3}$, provides reasonable explanation for our measurements and previous
findings at the X-ray and gamma-ray wavelengths. We find that the transition to
the Sedov-Taylor (ST) phase is incomplete for any reasonable set of parameters,
implying that the current maximum energy of accelerated protons in RX
J1713.7-3946 would not correspond to the maximum attainable energy for this
remnant.
