Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Superficial velocity and subject to assumptions. Superficial velocity can be expressed as: where: Using the concept of porosity, the dependence between the advection velocity and the superficial velocity can be expressed as (for one-dimensional flow): where: The local physical velocity can still be different than the average fluid velocity because the vector of the local fluid flow does not have to be parallel to that of average flow. Also, there may be local constriction in the flow channel. Superficial velocity Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity