− ∫∫ ρuq cos θ dS = − ∫∫ (lρu2 + mρuv + nρuw) dS,
(1)
which by Green’s transformation is
| − ∫∫∫ ( | d(ρu2) | + | d(ρuv) | + | d(ρuw) | ) dx dy dz. |
| dx | dy | dz |
(2)
The rate of generation of momentum in the interior of S by the component of force, X per unit mass, is
∫∫∫ ρX dx dy dz,
(3)
and by the pressure at the surface S is
| − ∫∫ lp dS = − ∫∫∫ | dp | dx dy dz, |
| dx |