  The Fornax Cluster is the nearest galaxy cluster in the southern sky. NGC
1404 is a bright elliptical galaxy falling through the intracluster medium of
the Fornax Cluster. The sharp leading edge of NGC 1404 forms a classical "cold
front" that separates 0.6 keV dense interstellar medium and 1.5 keV diffuse
intracluster medium. We measure the angular pressure variation along the cold
front using a very deep (670\,ksec) {\sl Chandra} X-ray observation. We are
taking the classical approach -- using stagnation pressure to determine a
substructure's speed -- to the next level by not only deriving a general speed
but also directionality which yields the complete velocity field as well as the
distance of the substructure directly from the pressure distribution. We find a
hydrodynamic model consistent with the pressure jump along NGC 1404's
atmosphere measured in multiple directions. The best-fit model gives an
inclination of 33$^{\circ}$ and a Mach number of 1.3 for the infall of NGC
1404, in agreement with complementary measurements of the motion of NGC 1404.
Our study demonstrates the successful treatment of a highly ionized ICM as
ideal fluid flow, in support of the hypothesis that magnetic pressure is not
dynamically important over most of the virial region of galaxy clusters.
