(7)
with two similar equations.
The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a numerical application it is assumed that C.G.S. units are intended.
These equations may be simplified slightly, using the equation of continuity (5) § 21; for
| dρu | + | dρu2 | + | dρuv | + | dρuw |
| dt | dx | dy | dz |
| = ρ ( | du | + u | du | + v | du | + w | du | ) |
| dt | dx | dy | dz |
| + u ( | dρ | + | dρu | + | dρv | + | dρw | ), |
| dt | dx | dy | dz |
(8)
reducing to the first line, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form
| du | + u | du | + v | du | + w | du | = X − | 1 | dp | , | |
| dt | dx | dy | dz | ρ | dx |