- #1
Hemmer
- 16
- 0
Hi there,
I have a question about incompressible Stokes flow in a channel between solid walls (with no-slip boundary conditions at ##y = 0, L_y##). It is my intuition that, if the flow direction is ##x## (periodic), and the direction normal to the walls is ##y##, then there cannot be a net velocity in that direction, i.e. ##\langle v_y \rangle = 0##, as this somehow implies fluid must be passing through the walls? Is this correct and if so how should I go about showing this? I guess it might require some integration of the incompressibility condition but I've not got anywhere yet. Full equations:
$$\eta\nabla^2 \textbf{v} - \nabla p = \textbf{f}, \qquad\nabla . \textbf{v}=0$$
Please let me know if you require any additional information, and any replies greatly appreciated!
I have a question about incompressible Stokes flow in a channel between solid walls (with no-slip boundary conditions at ##y = 0, L_y##). It is my intuition that, if the flow direction is ##x## (periodic), and the direction normal to the walls is ##y##, then there cannot be a net velocity in that direction, i.e. ##\langle v_y \rangle = 0##, as this somehow implies fluid must be passing through the walls? Is this correct and if so how should I go about showing this? I guess it might require some integration of the incompressibility condition but I've not got anywhere yet. Full equations:
$$\eta\nabla^2 \textbf{v} - \nabla p = \textbf{f}, \qquad\nabla . \textbf{v}=0$$
Please let me know if you require any additional information, and any replies greatly appreciated!