Ram pressure is a pressure exerted on a body moving through a fluid medium, caused by relative bulk motion of the fluid rather than random thermal motion. It causes a drag force to be exerted on the body. Ram pressure is given in tensor form as , where is the density of the fluid; is the momentum flux per second in the direction through a surface with normal in the direction. are the components of the fluid velocity in these directions. The total Cauchy stress tensor is the sum of this ram pressure and the isotropic thermal pressure (in the absence of viscosity). In the simple case when the relative velocity is normal to the surface, and momentum is fully transferred to the object, the ram pressure becomes . Derivation 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. Example - sea level ram air pressure What is the sea level ram air pressure at 100 mph? Imperial units ρ = .0023769 sea level air density (slugs/ft3) v2 = 1472 (100 mph = 147 ft/sec) P = 0.5 * ρ * v2 P = 25.68 (pressure in lbf/ft2) SI units ρ = 1.2250 sea level air density (kg/m3)