(4)
by Green’s transformation.
The time rate of increase of momentum of the fluid inside S is
| ∫∫∫ | d(ρu) | dx dy dz; |
| dt |
(5)
and (5) is the sum of (1), (2), (3), (4), so that
| ∫∫∫ ( | dρu | + | dρu2 | + | dρuv | + | dρuw | − ρX + | dp | ) dx dy dz = 0, |
| dt | dx | dy | dz | dx |
(6)
leading to the differential equation of motion
| dρu | + | dρu2 | + | dρuv | + | dρuw | = ρX − | dp | , |
| dt | dx | dy | dz | dx |