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) Chandra X-ray observation. We are taking the classical approach -- using

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... ion 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^∘ 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.