The Eulerian form of the Cauchy momentum equation for a fluid is
for isotropic pressure , where  is fluid velocity,  the fluid density, and  the gravitational acceleration. The Eulerian rate of change of momentum in direction  at a point is thus (using Einstein notation):
Substituting the conservation of mass, expressed as
this is equivalent to
using the product rule and the Kronecker delta . The first term in the brackets is the isotropic thermal pressure, and the second is the ram pressure.
In this context, ram pressure is momentum transfer by advection (flow of matter carrying momentum across a surface into a body). The mass per unit second flowing into a volume  bounded by a surface  is
and the momentum per second it carries into the body is
equal to the ram pressure term. This discussion can be extended to drag forces; if all matter incident upon a surface transfers all its momentum to the volume, this is equivalent (in terms of momentum transfer) to the matter entering the volume (the context above). On the other hand, if only velocity perpendicular to the surface is transferred, there are no shear forces, and the effective pressure on that surface increases by
where  is the velocity component perpendicular to the surface.