Page 16 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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1.2.1.1.2. Motion equations - equations of Navier-Stokes
The differential equations of Navier-Stokes are basic equations in fluid
dynamics. By solving them together with the equation of continuity for each of
the phases of a multi-phase flow system with the corresponding boundary
conditions, theoretically, it is possible to describe the hydrodynamie processes
in all technical and nature systems. The equations, written on the basis of a
balance of the forces of viscosity, gravity and inertia, are as follows.

For JC axis:

Dw, dp (^ 180
(20)
dt dx { 3

. . , , , , . , (21)
dt

For z axis:

2
$ W +l£^\ (22)
2
3 8z '

^, .„,,. , „ , . -Dw. Dw Bw,
The left-hand sides oi the equations p -, p — and p -
dt dt dt
Dw
express the product of the mass of a volume unit and its acceleration .
dt
On the right-hand sides of the equations, p.g expresses the influence
of the gravity force on the moving of the fluid. The partial derivatives
—,—and — denote the change of the fluid hydraulic pressure in direction
dx 8y dz
2
of the corresponding coordinate axis. The term w V w x -I and the
\ 3 dx)
corresponding terms for y and z coordinates take into account the friction forces
and the resulting contractive and tensile forces in viscous fluid.