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
Mass balance stoichiometric mass of air is , so AFR = 14.56. The combustion product mass is then . At exact stoichiometry, should be absent. At 15 percent excess air, the AFR = 16.75, and the mass of the combustion product gas is , which contains of excess oxygen. The combustion gas thus contains 2.84 percent by mass. The relationships between percent excess air and % in the combustion gas are accurately expressed by quadratic equations, valid over the range 0–30 percent excess air: In the second example we will use the law of mass action to derive the expression for a