  Stochastic monotonicity is a well known partial order relation between
probability measures defined on the same partially ordered set. Strassen
Theorem establishes equivalence between stochastic monotonicity and the
existence of a coupling compatible with respect to the partial order. We
consider the case of a countable set and introduce the class of \emph{finitely
decomposable flows} on a directed acyclic graph associated to the partial
order. We show that a probability measure stochastically dominates another
probability measure if and only if there exists a finitely decomposable flow
having divergence given by the difference of the two measures. We illustrate
the result with some examples. In fluid theory the Lagrangian description
follows the trajectories of the particles while the Eulerian one observes the
local flow. A coupling gives a Lagrangian description of the transference plan
of mass while a flow gives an Eulerian one
