(Book: 5.2)
As you may guess, Newton's second law is the most important equation for fluid flow, besides mass conservation. We will write Newton's law in the form of conservation of linear momentum.
The momentum equation in words: the rate of change of linear momentum of a material region equals the net force on the region:
The Lagrangian formulation is:
Note: by the definition of the center of gravity (mass, really), 
, where 
is the
velocity of the center of gravity, so we can also write the
momentum equation as
, which is Newton's law in the more
conventional form.
Note: the book says the momentum equation above cannot be derived from
Newton's equation for a point mass. However, setting
for an infinitesimal element of
fluid with volume 
and integrating using action = -reaction
does produce the momentum equation above.