Suppose i have two functions, one of mass flow and other of momentum flow through a surface: $$ f = \int_A \rho (v \cdot n)dA $$ $$ g = \int_A \rho v (v \cdot n)dA $$
$\rho$ = density of the material $v$ = velocity through the surface $n$ = normal vector to the surface $A$ = area of the surface
Is this allowed? $$ df = \rho (v \cdot n)dA $$ $$ g = \int vdf $$ $$ v_m f = \int vdf $$ $$ g = v_mf$$
If not, is there a meaningful way to get $f$ into the integral of $g$?