  Applying the Hamilton's quaternion algebra, we propose the generalized
electromagnetic-fluid dynamics of dyons governed by the combination of the
Dirac-Maxwell, Bernoulli and Navier-Stokes equations. The generalized
quaternionic hydro-electromagnetic field of dyonic cold plasma consist the
electrons and the magnetic monopoles in which there exist dual-mass and
dual-charge species in presence of dyons. We construct the conservation of
energy and conservation of momentum equations by equating the quaternionic
scalar and vector parts for generalized hydro-electromagnetic field of dyonic
cold plasma. We propose the quaternionic form of conservation of energy is
related to the Bernoulli's like equation while the conservation of momentum is
related to Navier-Stokes like equation for dynamics of dyonic plasma fluid.
Further, the continuity equation i.e. the conservation of electric and magnetic
charges with the dynamics of hydro-electric and hydro-magnetic flow of
conducting cold plasma fluid is also analyzed. The quaternionic formalism for
dyonic plasma wave emphasizes that there are two types of waves propagation
namely the Langmuir like wave propagation due to electrons, and the
t-Hooft-Polyakov like wave propagation due to magnetic monopoles.
