  We report a new kind of experiment in which we generate a known superfluid
velocity in a straight tube and directly determine the phase difference across
the tube's ends using a superfluid matter wave interferometer. By so doing, we
quantitatively verify the relation between the superfluid velocity and the
phase gradient of the condensate macroscopic wave function. Within the
systematic error of the measurement (~10%) we find v_s=(hbar/m_4)*(grad phi).
